Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption "Experts" in this Registration Statement (Form S-3) and related Prospectus of Infinity Pharmaceuticals, Inc. for the registration of $250 million of debt securities, common stock, preferred stock, units, and warrants  and to the incorporation by reference therein of our report dated March 16, 2021, with respect to the consolidated financial statements of Infinity Pharmaceuticals, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2020, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts

May 13, 2021