Exhibit 5.1

May 5, 2020

Karyopharm Therapeutics Inc.

85 Wells Avenue, 2nd Floor

Newton, MA 02459

Ladies and Gentlemen:

This opinion is being furnished to you in connection with (i) the Registration Statement on Form S-3 (File No. 333-236639) (the “Registration Statement”) filed by Karyopharm Therapeutics Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of, among other things, an indeterminate number of shares of Common Stock, $0.0001 par value per share, of the Company, which may be issued from time to time on a delayed or continuous basis pursuant to Rule 415 under the Securities Act, as set forth in the Registration Statement and the prospectus contained therein (the “Base Prospectus”) and (ii) the prospectus supplement, dated May 5, 2020 (the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”) relating to the issuance and sale from time to time by the Company of shares of Common Stock with an aggregate offering price of up to $100,000,000 (the “Shares”).

The Shares are to be issued and sold by the Company pursuant to an Open Market Sale Agreement, dated August 17, 2018, as amended by Amendment No. 1 to the Open Market Sale Agreement, dated as of May 5, 2020, (as amended, the “Sale Agreement”), between the Company and Jefferies LLC. We are acting as counsel for the Company in connection with the issue and sale by the Company of the Shares. We have examined copies of the Registration Statement and the Prospectus as filed with the Commission. We have also examined and relied upon the Sale Agreement, minutes of meetings of the stockholders and the Board of Directors of the Company, including committees thereof as provided to us by the Company, stock record books of the Company as provided to us by the Company, the Certificate of Incorporation and By-laws of the Company, each as restated and/or amended to date, and such other documents as we have deemed necessary for purposes of rendering the opinions hereinafter set forth.

In our examination of the foregoing documents, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of the originals of such latter documents and the legal competence of all signatories to such documents. Further, we have assumed that the Company will not issue and sell pursuant to the Sale Agreement such number of Shares that would cause the Company not to satisfy the eligibility requirements for Form S-3 (including Instruction I.B.6. thereof).

Karyopharm Therapeutics Inc.

May 5, 2020

Page 2

We express no opinion herein as to the laws of any state or jurisdiction other than the General Corporation Law of the State of Delaware and the federal laws of the United States of America.

Based upon and subject to the foregoing, we are of the opinion that the Shares have been duly authorized for issuance and, when the Shares are issued and paid for in accordance with the terms and conditions of the Sale Agreement, the Shares will be validly issued, fully paid and nonassessable.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act as an exhibit to the Current Report on Form 8-K to be filed by the Company on the date hereof in connection with the issuance and sale of the Shares and to the use of our name therein and in the related Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

WILMER CUTLER PICKERING

HALE AND DORR LLP