EXHIBIT 5.1

August 9, 2019

Acorda Therapeutics, Inc.

420 Saw Mill River Road

Ardsley, New York 10502

Ladies and Gentlemen:

We have acted as counsel to Acorda Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the registration by the Company under the Securities Act of 1933, as amended (the “Act”), of 1,500,000 shares of the Company’s Common Stock, par value $0.001 per share (the “Shares”), issuable under the Acorda Therapeutics, Inc. 2019 Employee Stock Purchase Plan (the “Plan”), pursuant to the registration statement on Form S-8 filed with the Securities and Exchange Commission on the date hereof (such registration statement is referred to herein as the “Registration Statement”).

We have reviewed such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals.

We have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible.

Based upon the foregoing, we are of the opinion that the Shares have been duly authorized and, when issued and paid for in accordance with the terms of the Company’s Certificate of Incorporation, the Plan and any individual agreements relating to such Shares, will be validly issued, fully paid and nonassessable.

We are members of the bar of the State of New York. We do not express any opinion herein on any laws other than the General Corporation Law of the State of Delaware and applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.

Sincerely,

/s/ Covington & Burling