Exhibit 5.1

June 13, 2016

Rice Midstream Partners LP

2200 Rice Drive

Canonsburg, Pennsylvania, 15317

RE: RICE MIDSTREAM PARTNERS LP

Ladies and Gentlemen:

We have acted as counsel to Rice Midstream Partners LP, a Delaware limited partnership (the “Partnership”), in connection with the registration by the Partnership with the Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and sale by the Partnership of 9,200,000 common units representing limited partner interests in the Partnership (the “Common Units”). We have participated in the preparation of a Prospectus Supplement dated June 7, 2016 (the “Prospectus Supplement”) and the Prospectus dated February 4, 2016 (the “Prospectus”) forming part of the Registration Statement on Form S-3 (No. 333-209089) (the “Registration Statement”). The Prospectus Supplement has been filed pursuant to Rule 424(b) promulgated under the Securities Act.

In rendering the opinions set forth below, we have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) an Underwriting Agreement, dated June 7, 2016 relating to the offering and sale of the Common Units (the “Underwriting Agreement”), a copy of which is being filed with the SEC as an exhibit to the Partnership’s Current Report on Form 8-K on or about the date hereof, (ii) the Registration Statement, (iii) the Prospectus Supplement, (iv) the Prospectus, (v) the Partnership’s Amended and Restated Agreement of Limited Partnership (the “Partnership Agreement”), (vi) the Partnership’s Certificate of Limited Partnership, (vii) the Amended and Restated Limited Liability Company Agreement of Rice Midstream Management LLC (the “General Partner”), the general partner of the Partnership, (viii) certain resolutions adopted on January 21, 2016 and June 1, 2016 by the board of directors of the General Partner and on June 7, 2016 by the pricing committee thereof approving and authorizing, among other things, the Registration Statement and other matters relating to the offering of the Common Units (the “Resolutions”) and (ix) such other certificates, statutes and other instruments and documents as we considered appropriate for purposes of the opinions hereafter expressed.

In connection with rendering the opinions set forth below, we have assumed that (i) all information contained in all documents reviewed by us is true and correct; (ii) all signatures on all documents examined by us are genuine; (iii) all documents submitted to us as originals are authentic and complete and all documents submitted to us as copies conform to the originals of those documents; (iv) the certificates for the Common Units will conform to the specimens thereof examined by us and will have been duly countersigned by a transfer agent and duly registered by a registrar of the Common Units; and (v) the Underwriting Agreement has been duly authorized and validly executed and delivered by the Underwriters and constitutes a legal, valid and binding obligation of the Underwriters, and that the Underwriters have the requisite organizational and legal power and authority to perform their obligations under the Underwriting Agreement.

Based on the foregoing and on such legal considerations as we deem relevant, we are of the opinion that when the Common Units have been issued and delivered in accordance with the terms of the Underwriting Agreement, the Prospectus Supplement, the Prospectus and the Resolutions and upon payment of the consideration therefor provided for therein, such Common Units will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by Section 17-303, 17-607 or 17-804 of the Delaware Revised Uniform Limited Partnership Act (the “DRULPA”)).

The opinions expressed is limited in all respects to the DRULPA and the Delaware Limited Liability Company Act (including, in each case, the applicable provisions of the Delaware Constitution and the reported judicial decisions interpreting these laws) and the federal laws of the United States of America, and we are expressing no opinion as to the effect of the laws of any other jurisdiction, domestic or foreign.

We hereby consent to the filing of this opinion of counsel as Exhibit 5.1 to the Current Report on Form 8-K of the Partnership dated on or about the date hereof, to the incorporation by reference of this opinion of counsel into the Registration Statement and to the reference to our firm under the heading “Legal Matters” in the Prospectus Supplement and the Prospectus. In giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC issued thereunder.