Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the Codiak BioSciences, Inc. 2015 Stock Option and Grant Plan, Codiak BioSciences, Inc. 2020 Stock Option and Incentive Plan, and Codiak BioSciences, Inc. 2020 Employee Stock Purchase Plan of our report dated August 6, 2020, except for Note 21(c) as to which the date is October 2, 2020, with respect to the consolidated financial statements of Codiak BioSciences, Inc. included in its Registration Statement (Form S-1 No. 333-248692) and related Prospectus of Codiak BioSciences, Inc., filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts

October 15, 2020