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-3 ASR No. 333-190568),

(2) Registration Statement (Form S-8 No. 333-116295) pertaining to the 2004 Stock Incentive Plan,

(3) Registration Statement (Form S-8 No. 333-135460) pertaining to the 2004 Stock Incentive Plan,

(4) Registration Statement (Form S-8 No. 333-152105) pertaining to the Amended and Restated 2004 Stock Incentive Plan,

(5) Registration Statement (Form S-8 No. 333-167895) pertaining to the Amended and Restated 2004 Stock Incentive Plan,

(6) Registration Statement (Form S-8 No. 333-167896) pertaining to the 2010 Employee Stock Purchase Plan,

(7) Registration Statement (Form S-8 No. 333-189710) pertaining to the 2013 Stock Incentive Plan,

(8) Registration Statement (Form S-8 No. 333-197986) pertaining to the 2013 Stock Incentive Plan,

(9) Registration Statement (Form S-8 No. 333-206250) pertaining to the 2013 Stock Incentive Plan,

(10) Registration Statement (Form S-3 ASR No. 333-209956), and

(11) Registration Statement (Form S-8 No. 333-212920) pertaining to the 2010 Employee Stock Purchase Plan and the 2013 Stock Incentive Plan;

of our reports dated February 27, 2019, with respect to the consolidated financial statements of The Medicines Company and the effectiveness of internal control over financial reporting of The Medicines Company included in this Annual Report (Form 10-K) of The Medicines Company for the year ended December 31, 2018.

/s/Ernst & Young LLP                                    

Iselin, New Jersey

February 27, 2019