EXHIBIT 5.1

212-373-3000 212-757-3990

June 28, 2019

The Medicines Company

8 Sylvan Way

Parsippany, New Jersey 07054

Registration Statement on Form S-3ASR(Registration No. 333-232317)

Ladies and Gentlemen:

We have acted as special counsel to The Medicines Company, a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-3ASR (File No. 333–232317) (the “Registration Statement”) of the Company, filed with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Act”), and the rules and regulations thereunder (the “Rules”).  You have asked us to furnish our opinion as to the legality of 5,227,273 shares of the Company’s common stock, par value $0.001 per share (the “Common Stock”) (including shares issuable by the Company upon exercise of the underwriters’ option to purchase additional

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shares of Common Stock), which are registered under the Registration Statement and which are being sold today pursuant to an Underwriting Agreement dated June 25, 2019 (the “Underwriting Agreement”), between Goldman Sachs & Co. LLC and J.P. Morgan Securities LLC, as representatives for the underwriters named on Schedule I thereto and the Company.

In connection with the furnishing of this opinion, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (collectively, the “Documents”):

1.          the Registration Statement;

2.          the preliminary prospectus supplement dated June 24, 2019 (the “Preliminary Prospectus”);

3.          the final prospectus supplement dated June 25, 2019 (the “Final Prospectus”); and

4.          the Underwriting Agreement.

In addition, we have examined (i) such corporate records of the Company that we have considered appropriate, including a copy of the certificate of incorporation, as amended, and by-laws, as amended, of the Company, certified by the Company as in effect on the date of this letter, and copies of resolutions of the board of directors of the Company (the “Board”) and the pricing committee of the Board relating to the issuance of the Common Stock, certified by the Company, and (ii) such other certificates, agreements and documents that we deemed relevant and necessary as a basis for the opinion expressed below.  We have also relied upon the factual matters contained in the

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representations and warranties of the Company made in the Documents and upon certificates of public officials and the officers of the Company.

In our examination of the documents referred to above, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the documents reviewed by us, the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as certified, photostatic, reproduced or conformed copies of valid existing agreements or other documents, the authenticity of all the latter documents and that the statements regarding matters of fact in the certificates, records, agreements, instruments and documents that we have examined are accurate and complete.

Based upon the above, and subject to the stated assumptions, exceptions and qualifications, we are of the opinion that the Common Stock has been duly authorized by all necessary corporate action on the part of the Company and, when issued, delivered and paid for as contemplated in the Registration Statement and in accordance with the terms of the Underwriter Agreement, will be validly issued, fully paid and non-assessable.

The opinion expressed above are limited to the General Corporation Law of the State of Delaware.  Our opinion is rendered only with respect to the laws, and the rules, regulations and orders under those laws, that are currently in effect.

We hereby consent to use of this opinion as an exhibit to the Registration Statement and to the use of our name under the heading “Legal Matters” contained in the base prospectus included in the Registration Statement, the Preliminary Prospectus and

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the Final Prospectus. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required by the Act or the Rules.

Very truly yours,

/s/ Paul, Weiss, Rifkind, Wharton & Garrison LLP

PAUL, WEISS, RIFKIND, WHARTON & GARRISON LLP