Exhibit 5.1

Goodwin Procter LLP
3025 John F Kennedy Blvd
Philadelphia, PA 19104
goodwinlaw.com
+1 (445) 207-7800

December 12, 2025

TELA Bio, Inc.

1 Great Valley Parkway, Suite 24

Malvern, Pennsylvania 19355

Re: Securities Registered under Registration Statement on Form S-3

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-3 (as amended or supplemented, the “Registration Statement”), filed on December 12, 2025, with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the offering by TELA Bio, Inc., a Delaware corporation (the “Company”), of up to 2,000,000 shares (the “Shares”) of the Company’s common stock, par value $0.001 per share (“Common Stock”), to be sold by the selling stockholder listed in the Registration Statement under “Selling Stockholder” (the “Selling Stockholder”). The Shares are issuable upon the exercise of an outstanding warrant to purchase shares of the Company’s Common Stock, which was originally issued by the Company in connection with that certain Credit Agreement and Guaranty dated as of November 13, 2025, by and between the Company and Perceptive Credit Holdings V, LP as lender and administrative agent (the “Warrant”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company. For purposes of the opinion set forth below, we have assumed that before the Shares are issued, the Company does not issue shares of Common Stock or reduce the total number of shares of Common Stock the Company is authorized to issue under its certificate of incorporation such that the number of unissued shares of Common Stock authorized under the Company’s certificate of incorporation is less than the number of Shares.

The opinion set forth below is limited to the Delaware General Corporation Law.

Based on the foregoing, we are of the opinion that, assuming the Shares were issued today in accordance with the terms of the Warrant, they would be validly issued, fully paid and nonassessable.

TELA Bio, Inc.

December 12, 2025

Page 2

The opinion expressed above is subject to bankruptcy, insolvency, fraudulent transfers, reorganization, moratorium and other similar laws of general application affecting the rights and remedies of creditors and to general principles of equity.

This opinion letter and the opinion it contains shall be interpreted in accordance with the Core Opinion Principles as published in 74 Business Lawyer 815 (Summer 2019).

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement and to the references to our firm under the caption “Legal Matters” in the Registration Statement. In giving our consent, we do not 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 thereunder.

Very truly yours,

/s/ Goodwin Procter LLP

GOODWIN PROCTER llp