Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

(1)Registration Statement (Form S-8 No. 333-249507) pertaining to the 2015 Stock Option and Grant Plan, 2020 Stock Option and Incentive Plan, and 2020 Employee Stock Purchase Plan of Codiak BioSciences, Inc.,

(2)Registration Statement (Form S-8 No. 333-254405) pertaining to the 2020 Stock Option and Incentive Plan of Codiak BioSciences, Inc., and

(3)Registration Statement (Form S-3 No. 333-260781) of Codiak BioSciences, Inc.;

of our report dated March 10, 2022, with respect to the consolidated financial statements of Codiak BioSciences, Inc. included in this Annual Report (Form 10-K) of Codiak BioSciences, Inc. for the year ended December 31, 2021.

/s/ Ernst & Young LLP

Boston, Massachusetts

March 10, 2022