Tetraphase Pharmaceuticals (TTPH) 8-K Tetraphase Pharmaceuticals Announces $17.5 Million of Financings PricedAt-the-Market

Exhibit 5.1

January 23, 2020 +1 617 526 6000 (t) +1 617 526 5000 (f) wilmerhale.com

Tetraphase Pharmaceuticals, Inc.

480 Arsenal Way

Watertown, MA 02472

Re: Registration Statement on FormS-3

Ladies and Gentlemen:

This opinion is being furnished to you in connection with (i) the Registration Statement on FormS-3 (FileNo. 333-222699) (the “Registration Statement”) filed by Tetraphase Pharmaceuticals, Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of, among other things, shares of Common Stock of the Company, par value $0.001 per share, and warrants to purchase Common Stock, which may be issued from time to time on a delayed or continuous basis pursuant to Rule 415 under the Securities Act for an aggregate initial offering price not to exceed $150,000,000, as set forth in the Registration Statement and the prospectus contained therein (the “Base Prospectus”), (ii) the preliminary prospectus supplement, dated January 22, 2020 (the “Preliminary Prospectus Supplement”) and (iii) the prospectus supplement, dated January 22, 2020 (the “Prospectus Supplement” and, together with the Base Prospectus and the Preliminary Prospectus Supplement, the “Prospectus”) relating to the issuance and sale pursuant to the Registration Statement of (i) up to2,380,105 shares of Common Stock (the “Shares”), (ii)pre-funded warrants (the“Pre-Funded Warrants”) to purchase up to an aggregate of 120,000 shares of Common Stock (the“Pre-Funded Warrant Shares”), and (iii) warrants (the “Common Stock Warrants” and together with thePre-Funded Warrants, the “Warrants”) to purchase up to an aggregate of 2,500,105 shares of Common Stock (the “Common Stock Warrant Shares”) and together with thePre-Funded Warrant Shares, the “Warrant Shares”). The Shares, the Warrants and the Warrant Shares are collectively referred to as the “Securities.”

The Securities are to be offered and sold by the Company pursuant to a securities purchase agreement dated January 22, 2020 (the “Purchase Agreement”), between the Company and the purchasers named therein, which is being filed with the Commission as Exhibit 10.1 to the Company’s Current Report on Form8-K, filed on the date hereof.

Tetraphase Pharmaceuticals, Inc.

January 23, 2020

Page 2

We are acting as counsel for the Company in connection with the issue and sale by the Company of the Securities. We have examined copies of the Registration Statement and Base Prospectus as filed, and Prospectus Supplement to be filed with the Commission. We have also examined and relied upon the Purchase Agreement, the Warrants, minutes of meetings of the stockholders and the Board of Directors of the Company as provided to us by the Company, the Certificate of Incorporation andBy-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.

We express no opinion herein as to the laws of any state or jurisdiction other than the state laws of the Commonwealth of Massachusetts, 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:

1. The Shares have been duly authorized for issuance and, when the Shares are issued and paid for in accordance with the terms and conditions of the Purchase Agreement, the Shares will be validly issued, fully paid and nonassessable.

2. The Warrants have been duly authorized for issuance and, when the Warrants are issued and paid for in accordance with the terms and conditions of the Purchase Agreement, the Warrants will have been duly executed and delivered by the Company and will constitute valid and legally binding obligations of the Company.

3. The Warrant Shares have been duly authorized for issuance and, when issued and paid for in accordance with the provisions of the Warrants, including the payment of the exercise price therefor, the Warrant Shares will be validly issued, fully paid andnon-assessable.

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.

Tetraphase Pharmaceuticals, Inc.

January 23, 2020

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We hereby consent to the filing of this opinion with the Commission, in accordance with the requirements of Item 601(b)(5) of RegulationS-K under the Securities Act, as an exhibit to the Current Report on Form8-K to be filed by the Company on the date hereof in connection with the issuance and sale of the Securities and to the use of our name therein and in the related Prospectus Supplement 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.

Sincerely,

WILMER CUTLER PICKERING HALE AND DORR LLP
By:	/s/ Stuart M. Falber
	Stuart M. Falber, a Partner