Exhibit 99.1

Epizyme Provides Business Update and Reports First Quarter 2021 Financial Results

Total Revenue of $7.6 Million for 1Q 2021; TAZVERIK^® Net Product Revenues of $6.2 Million

Ongoing TAZVERIK Clinical Trials in both Follicular Lymphoma and Prostate Cancer Demonstrate Encouraging Preliminary Safety and Activity Data

Investigational New Drug (IND) Submission for Novel SETD2 Inhibitor Program Planned for Mid-2021

Conference Call Today, Thursday, May 6 at 7:30 a.m. ET

CAMBRIDGE, Mass., May 6, 2021 – Epizyme (Nasdaq: EPZM), a fully integrated, commercial-stage biopharmaceutical company developing and delivering novel epigenetic therapies, today provided business and portfolio updates and reported first quarter 2021 financial results.

“Adoption of TAZVERIK has steadily increased as we continue to navigate the unique launch environment presented by COVID-19. We saw month-over-month commercial demand growth, with March 2021 representing our most successful month since launch and we look to build on this momentum as the pandemic-associated challenges begin to ease,” said Robert Bazemore, President and Chief Executive Officer of Epizyme. “TAZVERIK net revenues in the first quarter of 2021 increased by 37% from the fourth quarter of 2020, driven primarily by increased adoption in follicular lymphoma. The environment we operated in during the first quarter was not substantially different from the end of last year, however we are beginning to see some encouraging signs that things are slowly beginning to return to normal as vaccine adoption progresses.

“In early March, we hosted a strategic vision call to outline the pipeline-in-a-drug potential we see in TAZVERIK and plans to expand our portfolio starting with the anticipated IND submission for our novel SETD2 inhibitor in mid-2021. We plan to share additional pre-clinical data supporting the advancement of our SETD2 program at the European Hematology Association Congress 2021. During the Vision Call we also shared encouraging preliminary safety and activity data from ongoing combination trials in follicular lymphoma and prostate cancer and look forward to providing a steady stream of data updates from these and our many other planned and ongoing trials over the next few years.”

Recent Progress

Based on recent discussions with the U.S. Food and Drug Administration (FDA), Epizyme has aligned on an important change to the Phase 3 protocol whereby the second interim analysis will include an efficacy evaluation once 65% of progression free survival (PFS) events have occurred. This allows access to efficacy data earlier than previously expected and may provide an opportunity to stop the study early should the predefined treatment effect be realized. Based on these discussions with FDA, Epizyme has also expanded the Phase 1b portion of the study to include a minimum of 15 patients in the cohorts of 600 mg BID and 800 mg BID to help inform selection of the Phase 3 dose. Enrollment is nearly complete in these two cohorts and patients are being evaluated for follow-up of three months before initiating the Phase 3 randomization portion of the trial.

Preliminary data from the Phase 1b portion of this study has been accepted as a poster presentation at the 2021 ASCO Annual Meeting in June.

First Quarter 2021 Financial Results

2021 Financial Guidance

Conference Call Information

Epizyme will host a conference call today, May 6, at 7:30 a.m. ET. To participate in the conference call, please dial (877) 844-6886 (domestic) or (970) 315-0315 (international) and refer to conference ID 4139845. A webcast, as well as supplemental slides to support the webcast, will be available in the investor section of the Company’s website at www.epizyme.com, and will be archived for 60 days following the call.

About Non-GAAP Financial Measures

In addition to financial information prepared in accordance with the U.S. generally accepted accounting principles (GAAP), this press release includes the following non-GAAP financial measures: total non-GAAP adjusted operating expenses on a historical and projected basis, non-GAAP adjusted R&D expenses on a historical basis and non-GAAP adjusted SG&A expenses on a historical basis. Epizyme derives these non-GAAP financial measures by excluding certain expenses and other items from the respective GAAP financial measure, that is most directly comparable to each non-GAAP financial measure. Specifically, the non-GAAP financial measures exclude stock-based compensation expense and depreciation and amortization of intangibles. The company’s management believes that these non-GAAP financial measures are useful to both management and investors in analyzing its ongoing business and operating performance. Management does not intend the presentation of these non-GAAP financial measures to be considered in isolation or as a substitute for results prepared in accordance with GAAP, but as a complement to provide greater transparency. In addition, these non-GAAP financial measures may differ from similarly named measures used by other companies. A quantitative reconciliation of projected non-GAAP adjusted operating expenses to total operating expenses is not available without unreasonable effort primarily due to the company’s inability to predict with reasonable certainty the amount of future stock-based compensation expense.

About TAZVERIK^® (tazemetostat)

TAZVERIK is a methyltransferase inhibitor indicated for the treatment of:

These indications are approved under accelerated approval based on overall response rate and duration of response. Continued approval for these indications may be contingent upon verification and description of clinical benefit in confirmatory trials.

The most common (³20%) adverse reactions in patients with epithelioid sarcoma are pain, fatigue, nausea, decreased appetite, vomiting and constipation. The most common (³20%) adverse reactions in patients with follicular lymphoma are fatigue, upper respiratory tract infection, musculoskeletal pain, nausea and abdominal pain.

View the U.S. Full Prescribing Information here: Epizyme.com

About Epizyme, Inc.

Epizyme, Inc. is a fully integrated, commercial-stage biopharmaceutical company committed to its mission of rewriting treatment for cancer and other serious diseases through novel epigenetic medicines. In addition to an active research and discovery pipeline, Epizyme has one U.S. FDA approved product, TAZVERIK^® (tazemetostat), for the treatment of adults and pediatric patients aged 16 years and older with metastatic or locally advanced epithelioid sarcoma (ES) who are not eligible for complete resection; adult patients with relapsed or refractory follicular lymphoma (FL) whose tumors are positive for an EZH2 mutation as detected by an FDA-approved test and who have received at least two prior systemic therapies; and adult patients with relapsed or refractory follicular lymphoma who have no satisfactory alternative treatment options. These indications are approved under accelerated approval based on overall response rate and duration of response. Continued approval for these indications may be contingent upon verification and description of clinical benefit in confirmatory trials(s). The Company is also exploring the treatment potential of tazemetostat in investigational clinical trials in other solid tumors and hematological malignancies, as a monotherapy and combination therapy in both relapsed and front-line disease settings. By focusing on the genetic drivers of disease, Epizyme seeks to match medicines with the patients who need them. For more information, visit www.epizyme.com.

TAZVERIK^® is a registered trademark of Epizyme, Inc.

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: whether commercial sales of TAZVERIK for epithelioid sarcoma and follicular lymphoma in the approved indications will be successful; whether tazemetostat will receive marketing approval for epithelioid sarcoma or follicular lymphoma in other jurisdictions, full approval in the United States or approval in any other indication; whether results from preclinical studies or earlier clinical studies will be predictive of the results of future trials, such as the ongoing confirmatory trials; whether results from clinical studies will warrant meetings with regulatory authorities, submissions for regulatory approval or review by governmental authorities under the accelerated approval process; whether the company will receive regulatory approvals, including accelerated approval, to conduct trials or to market products; the impact of the COVID-19 pandemic on the company’s business, results of

operations and financial condition; whether the company’s cash resources will be sufficient to fund the company’s foreseeable and unforeseeable operating expenses and capital expenditure requirements; other matters that could affect the availability or commercial success of tazemetostat; and other factors discussed in the “Risk Factors” section of the company’s most recent Form 10-K or Form 10-Q filed with the SEC and in the company’s 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 and should not be relied upon as representing the company’s views as of any date subsequent to 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.

TAZVERIK^® is a registered trademark of Epizyme, Inc.

Contacts

Media:

Erin Graves

Epizyme, Inc.

Media@epizyme.com

(617) 500-0615

Investors:

Bill Slattery, Jr.

Real Chemistry

wslattery@realchemistry.com