Exhibit 5.1

One Financial Center Boston, MA 02111 617 542 6000 mintz.com

December 20, 2023

Aspen Aerogels, Inc.

30 Forbes Road, Building B

Northborough, MA 01532

Ladies and Gentlemen:

We have acted as counsel to Aspen Aerogels, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Prospectus Supplement, dated December 19, 2023, to a Prospectus, dated April 21, 2023 (collectively, the “Prospectus and Prospectus Supplement”), filed pursuant to a Registration Statement on Form S-3, as amended (Registration No. 333-263622) (the “Registration Statement”), pursuant to which the Company is offering for sale under the Securities Act of 1933, as amended (the “Securities Act”), an aggregate of 6,060,607 shares (the “Shares”) of its common stock, par value $0.00001 per share. The Shares are being sold pursuant to a Securities Purchase Agreement, dated as of December 19, 2023, among the Company and the investors named therein (the “Securities Purchase Agreement”), which will be filed as an exhibit to a Current Report on Form 8-K and incorporated by reference into the Registration Statement. All capitalized terms used herein and not otherwise defined shall have the respective meanings given to them in the Securities Purchase Agreement.

In connection with this opinion, we have examined the Company’s Restated Certificate of Incorporation, as amended, and the Company’s Restated Bylaws, each as currently in effect, such other records of the corporate proceedings of the Company and certificates of the Company’s officers as we have deemed relevant, as well as the Registration Statement and the exhibits thereto and the Prospectus, the Prospectus Supplement and the Securities Purchase Agreement.

In our examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, photostatic or facsimile copies and the authenticity of the originals of such copies.

Based upon the foregoing, and subject to the limitations set forth below, we are of the opinion that the Shares have been authorized for issuance, and when sold and issued and paid for in accordance with the Securities Purchase Agreement and in the manner contemplated by the Registration Statement and the Prospectus and Prospectus Supplement, will be validly issued, fully paid and nonassessable.

Our opinion is limited to the General Corporation Law of the State of Delaware. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

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.

BOSTON     LOS ANGELES     MIAMI     NEW YORK     SAN DIEGO     SAN FRANCISCO     TORONTO     WASHINGTON

MINTZ, LEVIN, COHN, FERRIS, GLOVSKY AND POPEO, P.C.

MINTZ   December 20, 2023 Page 2

We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act and to the use of this firm’s name therein and in the Prospectus and Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.

Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.

BOSTON     LOS ANGELES     MIAMI     NEW YORK     SAN DIEGO     SAN FRANCISCO     TORONTO     WASHINGTON

MINTZ, LEVIN, COHN, FERRIS, GLOVSKY AND POPEO, P.C.