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-1 No. 333-257747) of Trevi Therapeutics, Inc.,

(2)Registration Statements (Form S-3 Nos. 333-239499, 333-260279, 333-260820 and 333-264614) of Trevi Therapeutics, Inc.,

(3)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

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

of our report dated March 16, 2023, 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, 2022.

/s/ Ernst & Young LLP

Hartford, Connecticut

March 16, 2023