EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

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

(1)Registration Statement (Form S-3MEF No. 333-253026) of Infinity Pharmaceuticals, Inc.,

(2)Registration Statement (Form S-3 No. 333-230258) of Infinity Pharmaceuticals, Inc.,

(3)Registration Statement (Form S-3 No. 333-256096) of Infinity Pharmaceuticals, Inc.,

(4)Registration Statements (Form S-8 Nos. 333-167488 and 333-182005) pertaining to the Infinity Pharmaceuticals, Inc. 2010 Stock Incentive Plan,

(5)Registration Statements (Form S-8 Nos. 333-189342 and 333-205585) pertaining to the Infinity Pharmaceuticals, Inc. 2010 Stock Incentive Plan and the Infinity Pharmaceuticals, Inc. 2013 Employee Stock Purchase Plan,

(6)Registration Statement (Form S-8 No. 333-232110) pertaining to the Infinity Pharmaceuticals, Inc. 2019 Equity Incentive Plan and the Infinity Pharmaceuticals, Inc. 2013 Employee Stock Purchase Plan,

(7)Registration Statement (Form S-8 No. 333-257029) pertaining to the Infinity Pharmaceuticals, Inc. 2013 Employee Stock Purchase Plan, as amended,

(8)Registration Statement (Form S-8 No. 333-258360) pertaining to Nonqualified Stock Option Inducement Award and Restricted Stock Unit Inducement Award granted outside of the Registrant's 2019 Equity Incentive Plan, and

(9) Registration Statement (Form S-8 No. 333-260685) pertaining to Nonqualified Stock Option Inducement Award granted outside of the Registrant's 2019 Equity Incentive Plan;

of our report dated March 29, 2022, with respect to the consolidated financial statements of Infinity Pharmaceuticals, Inc. included in this Annual Report (Form 10-K) of Infinity Pharmaceuticals, Inc. for the year ended December 31, 2021.

/s/ Ernst & Young LLP

Boston, Massachusetts

March 29, 2022