Exhibit 5.1

July 7, 2021

+1 617 526 6000 (t)

+1 617 526 5000 (f)

wilmerhale.com

Trevi Therapeutics, Inc.

195 Church Street, 14th Floor

New Haven, Connecticut 06510

Ladies and Gentlemen:

This opinion is furnished to you in connection with a Registration Statement on Form S-1 (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of an aggregate of 5,170,088 shares (the “Shares”) of common stock, par value $0.001 per share (the “Common Stock”), of Trevi Therapeutics, Inc., a Delaware corporation (the “Company”) that have been or may be issued to Lincoln Park Capital Fund, LLC (the “Selling Stockholder”) pursuant to that certain Purchase Agreement, dated as of June 18, 2021, by and between the Company and the Selling Stockholder (the “Purchase Agreement”). All of the Shares are being registered for resale on behalf of the Selling Stockholder. The Shares consist of 170,088 outstanding shares of Common Stock that were issued to the Selling Stockholder on June 18, 2021 (the “Outstanding Shares”) and up to 5,000,000 shares of Common Stock (the “Purchase Shares”) that may be issued to the Selling Stockholder pursuant to the Purchase Agreement.

We are acting as counsel for the Company in connection with the registration for resale of the Shares. We have examined signed copies of the Registration Statement as filed with the Commission. We have also examined and relied upon the Purchase Agreement, minutes of meetings of the Board of Directors of the Company as provided to us by the Company, stock record books of the Company as provided to us by the Company, the Certificate of Incorporation and By-Laws of the Company, each as restated and/or amended to date, and such other documents as we have deemed necessary for purposes of rendering the opinions hereinafter set forth.

In our examination of the foregoing documents, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of the originals of such latter documents and the legal competence of all signatories to such documents.

Trevi Therapeutics, Inc.

July 7, 2021

Page 2

We assume that the appropriate action will be taken, prior to the offer and sale of the Shares by the Selling Stockholder, to register and qualify the Shares for sale under all applicable state securities or “blue sky” laws.

We express no opinion herein as to the laws of any state or jurisdiction other than the General Corporation Law of the State of Delaware and the federal laws of the United States of America.

Based upon and subject to the foregoing, we are of the opinion that the Shares have been duly authorized, the Outstanding Shares are validly issued, fully paid and nonassessable, and the Purchase Shares, when issued and paid for in accordance with the terms of the Purchase Agreement, will be validly issued, fully paid and nonassessable. It is understood that this opinion is to be used only in connection with the offer and sale of the Shares while the Registration Statement is in effect.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act and to the use of our name therein and in the related Prospectus under the caption “Legal Matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.