Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in the Registration Statement (Form S-3) and related Prospectus of Infinity Pharmaceuticals, Inc. for the registration of 1,134,689 shares of its common stock and to the incorporation by reference therein of our reports dated March 15, 2018, with respect to the consolidated financial statements of Infinity Pharmaceuticals, Inc., and the effectiveness of internal control over financial reporting of Infinity Pharmaceuticals, Inc., included in its Annual Report (Form 10-K) for the year ended December 31, 2017, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts

April 30, 2018