Martin Midstream Partners (MMLP) 8-K Martin Midstream Partners Announces Amendment To Revolving Credit Facility

Exhibit 99.3

Martin Midstream Partners L.P. Announces Cash Tender Offers for Any and All of Its

Outstanding 10.00% Senior Secured 1.5 Lien Notes Due 2024 and 11.50% Senior Secured

Second Lien Notes Due 2025

KILGORE, TX — January 30, 2023—Martin Midstream Partners L.P. (NASDAQ:MMLP) (“MMLP”) announced that it has commenced cash tender offers to purchase (i) any and all of the approximately $53.7 million outstanding aggregate principal amount of the 10.00% senior secured 1.5 lien notes due 2024 (the “2024 Notes”) issued by MMLP and its wholly owned subsidiary, Martin Midstream Finance Corp. (together with MMLP, the “Issuers”), and (ii) any and all of the approximately $291.4 million outstanding aggregate principal amount of the Issuers’ 11.50% senior secured second lien notes due 2025 (the “2025 Notes” and, together with the 2024 Notes, the “Existing Notes”), with a portion of the net proceeds from the Issuers’ concurrent private placement of $400 million in aggregate principal amount of senior secured second lien notes due 2028 (the “New Notes”), which was also announced today by MMLP. The tender offers are being made pursuant to an offer to purchase and related notice of guaranteed delivery, each dated as of January 30, 2023. The tender offers will expire at 5:00 p.m., New York City time, on February 3, 2023 (as such time and date may be extended, the “expiration time”). Tendered Notes may be withdrawn at any time before the expiration time.

Under the terms of the tender offers, holders of the Notes that are validly tendered and accepted at or prior to the expiration time, or holders who deliver to the depository and information agent a properly completed and duly executed notice of guaranteed delivery and subsequently deliver such Notes, each in accordance with the instructions described in the offer to purchase, will receive total cash consideration of $1,015.50 per $1,000 principal amount of 2024 Notes and $1,006.90 per $1,000 principal amount of 2025 Notes, plus an amount equal to any accrued and unpaid interest up to, but not including, the settlement date, which is expected to be February 8, 2023, subject to satisfaction of the Financing Condition described below.

The tender offers are contingent upon the satisfaction of certain conditions, including the condition that the Issuers shall have raised at least $400 million in gross proceeds from the offering of the New Notes on or prior to the settlement date (the “Financing Condition”). The tender offers are not conditioned on any minimum amount of Notes being tendered. MMLP may amend, extend or terminate either or both tender offers in its sole discretion.

To the extent any Notes remain outstanding after the consummation of the tender offers, the Issuers will exercise their optional redemption rights with respect to any outstanding Notes and satisfy and discharge each indenture governing the Notes (the “Indentures”), as applicable, on the settlement date, in accordance with the terms of the Indentures. Neither this statement nor the tender offers constitute a notice of redemption under the provisions of the Indentures.

The tender offers are being made pursuant to the terms and conditions contained in the offer to purchase and related notice of guaranteed delivery, each dated January 30, 2023, copies of which may be requested from the information agent for the tender offer, D.F. King & Co., Inc., at (800) 628-8510 (Toll-Free) or (212) 269-5550, by email at mmlp@dfking.com, or via the following web address: www.dfking.com/mmlp. Wells Fargo Securities, LLC will act as Dealer Manager for the tender offers. Questions regarding the tender offers may be directed to the Dealer Manager at (866) 309-6316 (toll-free) or (704) 410-4756 (collect).

This press release does not constitute a notice of redemption under the optional redemption provisions of the Indentures, nor does it constitute an offer to sell, or a solicitation of an offer to buy, any security, including the New Notes or the Existing Notes, nor does it constitute an offer, solicitation or sale in any jurisdiction in which such offer, solicitation or sale would be unlawful.

About MMLP

MMLP, headquartered in Kilgore, Texas, is a publicly traded limited partnership with a diverse set of operations focused primarily in the Gulf Coast region of the United States. MMLP’s primary business lines include: (1) terminalling, processing, storage, and packaging services for petroleum products and by-products; (2) land and marine transportation services for petroleum products and by-products, chemicals, and specialty products; (3) sulfur and sulfur-based products processing, manufacturing, marketing and distribution; and (4) natural gas liquids marketing, distribution, and transportation services.

Forward-Looking Statements

All statements in this release other than historical facts are forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. These forward-looking statements and all references to financial estimates rely on a number of assumptions concerning future events and are subject to a number of uncertainties, including (i) the effects of the continued volatility of commodity prices and the related macroeconomic and political environment, (ii) risks and uncertainties related to the capital markets generally, (iii) whether the Issuers will offer the New Notes or consummate the offering, (iv) the anticipated terms of the New Notes, (v) the anticipated use of proceeds, including the repurchase of the Notes, and (vi) other factors, many of which are outside its control, which could cause actual results to differ materially from such statements. While MMLP believes that the assumptions concerning future events are reasonable, it cautions that there are inherent difficulties in anticipating or predicting certain important factors. A discussion of these factors, including risks and uncertainties, is set forth in MMLP’s annual and quarterly reports filed from time to time with the Securities and Exchange Commission (the “SEC”). MMLP disclaims any intention or obligation to revise any forward-looking statements, including financial estimates, whether as a result of new information, future events, or otherwise except where required to do so by law.

Contact:

Sharon Taylor

Chief Financial Officer

(877) 256-6644

investor.relations@mmlp.com

2