Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” and to the use of our report dated March 6, 2019 (except for Note 16, as to which the date is April 29, 2019), in the Registration Statement (Form S-1) and related Prospectus of Codiak BioSciences, Inc. for the registration of its common stock.

/s/ Ernst & Young LLP

Boston, Massachusetts

April 29, 2019