Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

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

(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.;

of our report dated March 17, 2021, 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, 2020.

/s/ Ernst & Young LLP

Boston, Massachusetts

March 17, 2021