Exhibit 99.1

Epizyme Announces Second Quarter 2015 Financial Results and Provides Corporate Update

Cambridge, Mass., August 6, 2015 – Epizyme, Inc. (NASDAQ: EPZM), a clinical stage biopharmaceutical company creating novel epigenetic therapies for cancer patients, today reported business highlights and operating and financial results for the second quarter of 2015.

“As we enter the third quarter of 2015, Epizyme is in a strong position. Having regained global rights ex-Japan to tazemetostat, our lead clinical candidate, we are actively moving the program forward and expanding our clinical development activities,” said Robert Gould, Ph.D., President and Chief Executive Officer, Epizyme. “The company made significant progress advancing tazemetostat during the quarter. Importantly, we initiated the phase 2 NHL study and completed the transition of development-related transition activities from Eisai. Beyond tazemetostat, we look forward to working with Celgene on the three HMT targets defined under our renewed collaboration agreement. We are on strong financial footing and are well positioned to advance the development of our clinical programs and platform. As we announced yesterday, we have selected Rob Bazemore to succeed me as President and Chief Executive Officer, positioning us for continued success into the future.”

Program Summaries

Tazemetostat (EPZ-6438):

In the second quarter of 2015, Epizyme initiated a phase 2 monotherapy trial of its lead clinical candidate, tazemetostat, in patients with relapsed or refractory non-Hodgkin lymphoma (NHL). This five-arm study will enroll up to 150 patients with germinal center diffuse large B cell lymphoma (DLBCL) or follicular lymphoma, stratified by those expressing mutant EZH2 and those expressing wild type EZH2, as well as patients with non-germinal center DLBCL. The initial data from this study is expected in mid-2016.

The phase 1 study in relapsed or refractory NHL and advanced solid tumors is ongoing, with enrollment complete in the dose escalation and dose expansion cohorts. Enrollment in the clinical pharmacology portion of the study is ongoing. Epizyme will present updated data from patients with advanced solid tumors in the phase 1 study at ESMO’s European Cancer Congress in Vienna, Austria on September 26. Additional data from patients with NHL in the phase 1 study are expected to be presented at a medical meeting before the end of 2015. Results from the phase 1 trial presented at the International Congress on Malignant Lymphoma on June 20 showed tazemetostat as a monotherapy produced durable objective responses in heavily pre-treated patients with relapsed or refractory NHL, with an acceptable safety and tolerability profile.

Epizyme intends to initiate a phase 1 clinical study in pediatric patients with INI1-negative tumors or synovial sarcoma and a phase 2 clinical study in adult patients with INI1-negative tumors or synovial sarcoma in the second half of 2015.

Pinometostat (EPZ-5676):

Epizyme will voluntarily cease patient enrollment into the phase 1 study of pinometostat in adult patients with MLL-rearranged acute leukemia in the third quarter of 2015. The decision, made together with Celgene, is based on insufficient efficacy seen to date with monotherapy treatment in this population. The company expects to present final study results after all patients conclude treatment and data analyses are complete. A separate dose-escalation study of pinometostat in pediatric patients is ongoing and enrollment is expected to be completed in the second half of 2015.

Epizyme and Celgene plan to explore pinometostat in combination with other agents based on encouraging preclinical data.

Celgene collaboration update

Subsequent to the second quarter, Epizyme amended and restated its agreement with Celgene Corporation to extend the research collaboration between the two companies for at least three additional years. Epizyme received a $10 million upfront payment in exchange for an extension of Celgene’s option rights to individually license global rights for two histone methyltransferase (HMT) targets and ex-US rights for a third HMT target. Celgene may exercise its option with respect to each of the targets at the time of the IND filing for a pre-specified license payment. Following the completion of phase 1, if Celgene chooses to continue its license for a specific target, it may do so by making an additional pre-specified license payment.

Epizyme will be responsible for leading and funding development for each target candidate through phase 1 clinical trials. Epizyme may earn total potential milestones of up to $610 million on the three targets, including up to $75 million in development milestones and license fees, $365 million in regulatory milestones, and $170 million in sales milestones. Epizyme also may earn a royalty of up to a low double-digit percentage

on worldwide net product sales relating to two of the targets, and on ex-US annual net sales relating to the third target. Epizyme retains global rights to the remainder of its preclinical pipeline.

Second Quarter 2015 Financial Results

Collaboration Revenue: Collaboration revenue was $0.7 million in the second quarter of 2015 and $1.6 million for the six months ended June 30, 2015 compared with $9.5 million and $22.9 million in the comparable periods of 2014. The decline in collaboration revenue primarily reflects the completion of our research obligations under the Eisai agreement by the end of 2014 and under the GSK agreement by January 2015, as well as a decrease in revenue recognized under the Celgene agreement due to the Company’s satisfaction of certain of its performance obligations under the agreement during Q4 2014.

R&D Expenses: Research and development expenses were $20.6 million for the second quarter 2015 and $77.6 million for the six months ended June 30, 2015 compared to $17.5 million and $32.8 million for the comparable periods of 2014. The expansion of tazemetostat clinical trials and related EZH2 activities and the $40.0 million upfront payment to Eisai in the first quarter of 2015 drove the increase in spending in comparison to the three and six months ended June 30, 2014. Epizyme expects development expenses will continue to increase in 2015 as compared to 2014 since the Company is now solely responsible for funding tazemetostat clinical trials and related development costs outside of Japan.

G&A Expenses: General and administrative expenses were $6.0 million for the second quarter 2015 and $11.2 million for the six months ended June 30, 2015 compared with $5.3 million and $10.3 million in the comparable periods in 2014. The increase in G&A expense was largely related to the increased infrastructure to support the expanding clinical development program and an increase in patent filings. We expect G&A expense to increase slightly as compared to current spending levels for the remainder of 2015.

Net Loss: Net loss was $25.8 million in the second quarter 2015 and $87.1 million for the six months ended June 30, 2015 compared with $13.4 million and $20.3 million in the comparable periods in 2014.

Cash and Cash Equivalents: Cash and cash equivalents as of June 30, 2015 were $236.7 million, compared with $190.1 million as of December 31, 2014. Epizyme’s follow-on public offering in March 2015 raised $117.0 million in proceeds before expenses and the exercise of the underwriters’ over-allotment option provided an additional $13.7 million in proceeds before expenses. The company received an upfront payment of $10.0 million under the amended and restated collaboration and license agreement with Celgene in July 2015. The company expects that, based on its current operating plan, cash and equivalents will be sufficient to fund its operating expenses and capital expenditure requirements through at least the end of the second quarter of 2017 prior to including any potential license fees or future milestone payments.

Shares Outstanding: Shares outstanding as of June 30, 2015 were 41.2 million. Weighted average shares outstanding were 41.1 million and 38.1 million for the three and six months ended June 30, 2015 respectively and 33.2 million and 32.1 million for the comparable periods in 2014.

Conference Call Information

Epizyme will host a conference call and live audio webcast today at 7:30 a.m. ET to discuss second quarter 2015 financial results and provide a corporate update. To participate in the conference call, please dial (877) 844-6886 (domestic) or (970) 315-0315 (international) and refer to conference ID 90027895. The live webcast can be accessed under “Events and Presentations” in the Investor Relations section of the Company’s website at www.epizyme.com

The archived webcast will be available on the Company’s website beginning approximately two hours after the event.

About Epizyme, Inc.

Epizyme, Inc. is a clinical stage biopharmaceutical company creating novel epigenetic therapeutics for cancer patients. Epizyme has built a proprietary product platform that the Company uses to create small molecule inhibitors of a 96-member class of enzymes known as histone methyltransferases, or HMTs. HMTs are part of the system of gene regulation, referred to as epigenetics, that controls gene expression. Genetic alterations can result in changes to the activity of HMTs, making them oncogenic (cancer-causing). By focusing on the genetic drivers of cancers, Epizyme’s targeted science seeks to match the right medicines with the right patients.

For more information, visit www.epizyme.com and connect with us on Twitter at @EpizymeRx.

About EZH2 in Cancer

EZH2 is a histone methyltransferase (HMT) that is increasingly understood to play a potentially oncogenic role in a number of cancers. These include non-Hodgkin lymphomas, INI1-negative cancers such as malignant rhabdoid tumors, epithelioid sarcomas, synovial sarcoma, and a range of other solid tumors.

About Tazemetostat

Epizyme is developing tazemetostat for the treatment of non-Hodgkin lymphoma patients, patients with INI1-negative tumors or synovial sarcoma. Tazemetostat is a first-in-class small molecule inhibitor of EZH2 created by Epizyme using its proprietary product platform. In many human cancers, aberrant EZH2 enzyme activity results in misregulation of genes that control cell proliferation resulting in the rapid and unconstrained growth of tumor cells. Tazemetostat is the WHO International Non-Proprietary Name (INN) for compound EPZ-6438.

Tazemetostat is the second HMT inhibitor to enter human clinical development (following Epizyme’s DOT1L inhibitor, pinometostat, also known as EPZ-5676). The phase 1 and phase 2 portions of the clinical study of tazemetostat are ongoing, with additional data from the phase 1 portion expected to be reported later in 2015.

Additional information about this program, including clinical trial information, may be found here: https://clinicaltrials.gov/ct2/show/NCT01897571.

About Pinometostat

Epizyme is developing pinometostat, a small molecule inhibitor of DOT1L created with Epizyme’s proprietary product platform, for the treatment of patients with acute leukemia in which the MLL gene is rearranged due to a chromosomal translocation (MLL-r). Due to these rearrangements, DOT1L is misregulated, resulting in the increased expression of genes causing leukemia. Pinometostat is the WHO International Non-Proprietary Name (INN) for compound EPZ-5676.

Epizyme believes that pinometostat was the first HMT inhibitor to enter human clinical development. Epizyme is currently conducting a two-stage Phase 1 study in adult MLL-r patients and in May 2014, initiated a Phase 1b study of pinometostat in pediatric patients with rearrangements of the MLL gene. Additional information about this ongoing Phase 1 study can be found here: https://clinicaltrials.gov/ct2/show/NCT01684150.

Pinometostat has been granted orphan drug designation for the treatment of acute lymphoblastic leukemia (ALL) and acute myeloid leukemia (AML) by the Food and Drug Administration in the U.S. and by the European Commission in Europe.

Epizyme retains all U.S. rights to pinometostat and has granted Celgene an exclusive license to pinometostat outside of the U.S.

Cautionary Note on Forward-Looking Statements

Any statements in this press release about future expectations, plans and prospects for Epizyme, Inc. and other statements containing the words “anticipate,” “believe,” “estimate,” “expect,” “intend,” “may,” “plan,” “predict,” “project,” “target,” “potential,” “will,” “would,” “could,” “should,” “continue,” and similar expressions, constitute forward-looking statements within the meaning of The Private Securities Litigation Reform Act of 1995. Actual results may differ materially from those indicated by such forward-looking statements as a result of various important factors, including: uncertainties inherent in the initiation of future clinical studies or expansion of ongoing

clinical studies, availability and timing of data from ongoing clinical studies, whether interim results from a clinical trial will be predictive of the final results of the trial or the results of future trials, expectations for regulatory approvals, development progress of the Company’s companion diagnostics, availability of funding sufficient for the Company’s foreseeable and unforeseeable operating expenses and capital expenditure requirements, other matters that could affect the availability or commercial potential of the Company’s therapeutic candidates or companion diagnostics and other factors discussed in the “Risk Factors” section of our Form 10-Q most recently filed with the SEC, and in our other filings from time to time with the SEC. In addition, the forward-looking statements included in this press release represent the Company’s views as of the date hereof. The Company anticipates that subsequent events and developments will cause the Company’s views to change. However, while the Company may elect to update these forward- looking statements at some point in the future, the Company specifically disclaims any obligation to do so. These forward-looking statements should not be relied upon as representing the Company’s views as of any date subsequent to the date hereof.

EPIZYME, INC.

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Media/Investors:

Andrew Singer

Executive Vice President and Chief Financial Officer

Epizyme, Inc.

617.500.0712

asinger@epizyme.com