424B3

Filed Pursuant to Rule 424(b)(3)

Registration No. 333- 253117

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Warrants to Purchase 9,063 Shares of Common Stock

(and up to 9,063 Shares of Common Stock Issuable Upon Exercise of Such Warrants)

This prospectus supplement, dated December 2, 2022 (“Supplement”), filed by Baudax Bio, Inc. (the “Company”), modifies and supplements certain information contained in the Company’s prospectus supplement, dated December 27, 2021 (as amended and supplemented on August 25, 2022, and as may be further amended and supplemented from time to time, the “Prospectus Supplement”), as part of the Company’s Form S-3 Registration Statement declared effective by the Securities and Exchange Commission on September 2, 2021. This Supplement is not complete without, and may not be delivered or used except in connection with, the Prospectus Supplement, including all amendments and supplements thereto. The Prospectus Supplement relates to offering of warrants to purchase up to 9,063 shares of our common stock and this Supplement relates to 5,143 warrants that were sold in that offering (collectively, the “Warrants”) (and the shares of common stock issuable from time to time upon exercise of these warrants) pursuant to the terms of a securities purchase agreement that we entered into on December 27, 2021.

On August 2, 2022, the Company entered into a warrant amendment agreement with a certain holder of the Warrants (the “Amendment”) whereby the Company agreed to amend the Warrants held by such holder by reducing the exercise price of the Warrants held by such holder to $4.50 per share of common stock and agreed to extend the original expiration date of the Warrants held by such holder to December 6, 2027.

Accordingly, this Supplement amends and supplements the Prospectus Supplement to reflect (i) an amendment of the exercise price of the Warrants from $23.92 per share of common stock to $4.50 per share of common stock and (ii) the extension of the expiration date of the Warrants to December 6, 2027, each in accordance with the terms of the Amendment and all references in the Prospectus Supplement to (a) the exercise price with respect to the Warrants and (b) the expiration date with respect to the Warrants, are hereby amended and restated to reflect an exercise price of $4.50 per share of common stock and an expiration date of December 6, 2027. Following the Amendment, if all of the amended Warrants are exercised for cash, we would receive gross proceeds of approximately $23,000.

The information in this Supplement modifies and supersedes, in part, the information contained in the Prospectus Supplement. Any information that is modified or superseded in the Prospectus Supplement shall not be deemed to constitute a part of the Prospectus Supplement, except as so modified or superseded by this Supplement. We may further amend or supplement the Prospectus Supplement from time to time by filing additional amendments or supplements. You should read the entire Prospectus Supplement and any amendments or supplements carefully before you make an investment decision.

The Company’s common stock is traded on the Nasdaq Capital Market under the symbol “BXRX.” On December 1, 2022 the closing sale price of the Company’s common stock was $4.50 per share.

Investing in our common stock involves a high degree of risk. You should review carefully the risks and uncertainties described under the heading “Risk Factors” contained in the Prospectus Supplement, in our Annual Report on Form 10-K for the year ended December 31, 2021, and in our subsequently filed periodic and current reports and documents incorporated by reference therein and herein, which we file with the Securities and Exchange Commission, which describe specific risks and other information that should be considered before you make an investment decision.