Exhibit 5.1

One Financial Center Boston, MA 02111 617 542 6000 mintz.com

September 13, 2022

Codiak BioSciences, Inc.

35 CambridgePark Drive, Suite 500

Cambridge, Massachusetts 02140

Ladies and Gentlemen:

We have acted as legal counsel to Codiak BioSciences, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Prospectus Supplement, dated September 12, 2022 (the “Prospectus Supplement”), to a Registration Statement (File No. 333-260781) on Form S-3 (the “Registration Statement”), filed by the Company with the Commission under the Securities Act of 1933, as amended (the “Securities Act”). The Prospectus Supplement relates to the sale of an aggregate of 13,333,333 shares (the “Shares”) of the Company’s common stock, $0.0001 par value per share (the “Common Stock”) and accompanying warrants to purchase 13,333,333 shares of Common Stock (the “Warrants,” and together with the Common Stock, the “Securities”), including 1,999,999 shares of Common Stock and Warrants to purchase 1,999,999 shares of Common Stock subject to the underwriter’s option to purchase additional Securities, to Jefferies LLC as the underwriter (the “Underwriter”), pursuant to an Underwriting Agreement dated September 12, 2022 between the Company and the Underwriter (the “Underwriting Agreement”). The shares of Common Stock issuable upon exercise of the Warrants are hereinafter referred to as the “Warrant Shares.” The Underwriting Agreement will be filed as an exhibit to a Current Report on Form 8-K and incorporated by reference into the Registration Statement. This opinion is being rendered in connection with the filing of the Prospectus Supplement with the Commission. All capitalized terms used herein and not otherwise defined shall have the respective meanings given to them in the Registration Statement.

In connection with this opinion, we have examined the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated By-laws, each as currently in effect, the Registration Statement and the exhibits thereto, the Prospectus Supplement, the Underwriting Agreement and the Warrants and such other records of the corporate proceedings of the Company and certificates of the Company’s officers as we have deemed relevant.

In our examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, 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 copies, and the truth and correctness of any representations and warranties contained therein.

BOSTON    LONDON    LOS ANGELES    NEW YORK    SAN DIEGO    SAN FRANCISCO    WASHINGTON

MINTZ, LEVIN, COHN, FERRIS, GLOVSKY AND POPEO, P.C.

MINTZ   September 13, 2022 Page 2

Our opinion expressed herein is limited to the General Corporation Law of the State of Delaware and we express no opinion with respect to the laws of any other jurisdiction. No opinion is expressed herein with respect to the qualification of the Securities or Warrant Shares under the securities or blue sky laws of any state or any foreign jurisdiction. With respect to the Warrant Shares, we express no opinion to the extent that, notwithstanding its current reservation of shares of Common Stock, future issuances of securities, including the Warrant Shares, and/or antidilution adjustments to outstanding securities of the Company, including the Warrants, may cause the Warrants to be exercisable for more shares of Common Stock than the number that then remain authorized but unissued.

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.

Based upon the foregoing, we are of the opinion that (i) the Shares, when issued and delivered in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and non-assessable, (ii) the Warrants, if and when paid for in accordance with the terms of the Registration Statement and the Underwriting Agreement, will constitute valid and legally binding obligations of the Company, except as may be limited by bankruptcy, insolvency or other similar laws affecting the rights and remedies of creditors in general and the general principles of equity and (iii) with respect to Warrant Shares issuable upon exercise of the Warrants when the exercise price is paid in full and the Warrant Shares are issued in accordance with the terms and conditions of the Warrants, will be validly issued, fully paid and non-assessable.

We understand that you wish to file this opinion with the Commission as an exhibit to a Current Report on Form 8-K for incorporation by reference into the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K promulgated under the Securities Act and to reference the firm’s name under the caption “Legal Matters” in the Prospectus Supplement, and we hereby consent thereto. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.

Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.