Exhibit 5.1

March 14, 2018

Rhythm Pharmaceuticals, Inc.

500 Boylston Street, 11th Floor

Boston, MA 02116

Re:Registration Statement on Form S-8; 1,091,366 shares of Common Stock of Rhythm Pharmaceuticals, Inc., par value $0.001 per share

Ladies and Gentlemen:

We have acted as counsel to Rhythm Pharmaceuticals, Inc., a Delaware corporation (the “Company”), in connection with the registration by the Company of 1,091,366 shares of common stock of the Company, par value $0.001 per share (the “Shares”), issuable under the Company’s 2017 Equity Incentive Plan (the “EIP”).

The Shares are included in a registration statement on Form S-8 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on March 14, 2018 (the “Registration Statement”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or the related prospectuses, other than as expressly stated herein with respect to the issuance of the Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws.

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof, when the Shares shall have been issued and registered on the books of the transfer agent against payment therefor in the circumstances contemplated by the EIP, assuming that the individual issuances, grants or awards under the EIP are duly authorized by all necessary corporate action and duly issued, granted or awarded and exercised in accordance with the requirements of law and the EIP (and the agreements and awards duly adopted thereunder and in accordance therewith), the issue and sale of the Shares will have been duly authorized by all necessary corporate action of the Company, and the Shares will be validly issued, fully paid and nonassessable. In rendering the foregoing opinion, we have assumed that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Registration Statement. In giving such consent, we do not thereby

admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ MORGAN LEWIS & BOCKIUS LLP