Exhibit 5.1

June 23, 2014

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 filing of a Registration Statement on Form S-3 (File No. 333-196803) (as amended or supplemented, the “Registration Statement”) filed on June 16, 2014, with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Act”), relating to the registration of the offer by the Company of any combination of securities of the types specified therein. Reference is made to our opinion letter dated June 16, 2014, and included as Exhibit 5.1 to the Registration Statement. The Registration Statement became effective upon filing with the Commission. We are delivering this supplemental opinion letter in connection with the prospectus supplement (the “Prospectus Supplement”) filed on June 19, 2014, by the Company with the Commission pursuant to Rule 424 under the Securities Act. The Prospectus Supplement relates to the offering by the Company of (i) of up to $345,000,000 aggregate principal amount of its 1.75% Convertible Senior Notes due 2021 (the “Notes”), and (ii) the shares of the Company’s Common Stock that may be issued upon conversion of the Notes (the “Conversion Shares,” and collectively with the Notes, the “Securities”) covered by the Registration Statement. We understand that the Securities were offered and sold in the manner described in the Prospectus Supplement.

The Notes were issued by the Company pursuant to an indenture, dated June 23, 2014, by and between the Company and Wilmington Trust, National Association, as trustee (the “Trustee”), as supplemented by the first supplemental indenture, dated June 23, 2014, by and between the Company and the Trustee, establishing the terms of the Notes, in a form consistent with that authorized by the Company (as supplemented, the “Indenture”).

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.

Acorda Therapeutics, Inc.

June 23, 2014

Page 2

We have assumed further that the Trustee has duly authorized, executed and delivered the Indenture.

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 on the foregoing and subject to the qualification set forth below, we are of the opinion that:

1. The Notes have been duly issued and delivered against payment therefor as contemplated in the Registration Statement, and the Notes constitute the valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

2. The Conversion Shares initially issuable upon conversion of the Notes have been duly authorized and reserved for issuance and, when issued upon such conversion in accordance with the terms of the Notes and the Indenture, will be validly issued, fully paid and non-assessable.

We express no opinion as to provisions for liquidated damages and penalties or penalty interest.

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 law of the State of New York, the Delaware General Corporation Law, 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. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the Prospectus Supplement. 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.

Very truly yours,

/s/ Covington & Burling LLP