Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

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

(1)Registration Statements (Form S-3 Nos. 333-260279, 333-260820, 333-264614 and 333-273030) of Trevi Therapeutics, Inc.,

(2)Registration Statement (Form S-8 No. 333-231260) pertaining to the 2012 Stock Incentive Plan, as amended, the 2019 Stock Incentive Plan and the 2019 Employee Stock Purchase Plan of Trevi Therapeutics, Inc., and

(3)Registration Statements (Form S-8 Nos. 333-237193, 333-257729, 333-264615 and 333-271839) pertaining to the 2019 Stock Incentive Plan and the 2019 Employee Stock Purchase Plan of Trevi Therapeutics, Inc.;

of our report dated March 20, 2024, with respect to the consolidated financial statements of Trevi Therapeutics, Inc. included in this Annual Report (Form 10-K) of Trevi Therapeutics, Inc. for the year ended December 31, 2023.

/s/ Ernst & Young LLP

Hartford, Connecticut

March 20, 2024