Exhibit 99.1

MARTIN MIDSTREAM PARTNERS L.P. ANNOUNCES ENTRY INTO RESTRUCTURING SUPPORT AGREEMENT

KILGORE, Texas, June 26, 2020 (GLOBE NEWSWIRE) – Martin Midstream Partners L.P. (Nasdaq: MMLP) (the “Partnership”) today announced that it, its general partner, Martin Midstream GP LLC, and its subsidiaries Martin Midstream Finance Corp. (“FinanceCo”), Martin Operating GP LLC, Martin Operating Partnership L.P., Redbird Gas Storage LLC, Talen’s Marine & Fuel, LLC and Martin Transport, Inc. (together with the Partnership and FinanceCo, collectively, the “Company”) have entered into a restructuring support agreement (the “Restructuring Support Agreement”) with holders (the “Supporting Holders”) that beneficially own over 62% in principal amount of the Partnership and FinanceCo’s 7.25% Unsecured Notes due 2021 (the “Existing Notes”).

Ruben Martin, President and Chief Executive Officer of Martin Midstream GP LLC, the general partner of the Partnership stated “The Restructuring Support Agreement demonstrates the confidence our bondholders have in our leadership team and the vision we have for the Company. The transactions contemplated in this agreement offer the opportunity to increase our financial flexibility allowing the Company to concentrate on providing value to our business partners and unitholders. In these times of both macroeconomic and social challenges, we are appreciative of the support of the bondholders for our long-term success.”

The Restructuring Support Agreement contemplates that the Partnership and FinanceCo will commence an out-of-court exchange offer (the “Exchange Offer”) to exchange Existing Notes for a combination of cash, 11.50% Senior Secured Second Lien Notes due 2025 (the “Exchange Notes”), and rights to acquire 10.00% Senior Secured 1.5 Lien Notes due 2024 (the “New Notes”), subject to the terms and conditions of the Restructuring Support Agreement. In connection with the Exchange Offer, the Company will also commence a consent solicitation to make certain proposed amendments to the terms of the indenture governing the Existing Notes by eliminating or modifying certain restrictive covenants and other provisions. There are various closing conditions contemplated under the Restructuring Support Agreement including, among other things, the negotiation of definitive documentation and a minimum tender condition of 95% in principal amount of the Existing Notes in the Exchange Offer and consent solicitation.

As an alternative to the Exchange Offer, the Company agreed in the Restructuring Support Agreement to solicit acceptances from eligible holders of the Existing Notes of a prepackaged plan of reorganization (the “Prepackaged Plan”). In the event certain conditions to the Exchange Offer are not satisfied, and if a sufficient number of holders and amount of Existing Notes vote to accept the Prepackaged Plan, the Company intends to file petitions under chapter 11 of the U.S. Bankruptcy Code and pursue an in-court restructuring to implement the transactions contemplated herein.

Pursuant to the Restructuring Support Agreement, the Supporting Holders have agreed to, among other things, support and use commercially reasonable efforts to complete the financial restructuring, including by tendering their Existing Notes in the Exchange Offer, delivering their consents in the related consent solicitation and voting in favor of the Prepackaged Plan. The Restructuring Support Agreement may be terminated by the Supporting Holders or the Company upon the occurrence of certain events enumerated in the Restructuring Support Agreement. In connection with the Restructuring Support Agreement and subject to agreement upon mutually acceptable definitive documentation, the Supporting Holders are agreeing to purchase any unsubscribed New Notes that have not been purchased by eligible holders in the rights offering as part of the Exchange Offer, or if the Exchange Offer and related Cash Tender Offer are not consummated, pursuant to the Prepackaged Plan.

The purposes of the Exchange Offer and the issuance of the Exchange Notes and New Notes are to extend the maturities of the Company’s indebtedness.

The foregoing description of the Restructuring Support Agreement is qualified by reference to the full text of such agreement, a copy of which is included as Exhibit 10.1 to the Partnership’s Current Report on Form 8-K filed today.

The Company expects to continue the operation of its business in the ordinary course and does not anticipate interruption in its operations during the restructuring regardless of whether the Company conducts its restructuring in or out of the chapter 11 process. The transactions contemplated by the Restructuring Support Agreement are not

intended to impact trade vendors, employees, customers, or any related contractual agreements or obligations. The Partnership’s common units will remain outstanding and are not a part of the transactions contemplated by the Restructuring Support Agreement. The Company also expects to continue to have access to all necessary funds under its revolving credit facility, subject to the amendment of such revolving credit facility and receiving any related consents from its lenders.

The Exchange Offer will be made, and the Exchange Notes and New Notes will be offered and issued within the United States only to “qualified institutional buyers” as defined in Rule 144A under the Securities Act of 1933, as amended (the “Securities Act”) and institutional “accredited investors,” as defined in Rule 501 under the Securities Act and outside the United States to non-U.S. investors. The Exchange Notes and New Notes to be offered will not be registered under the Securities Act and may not be offered or sold in the United States absent registration or an applicable exemption from registration requirements.

This press release is for informational purposes only and does not constitute an offer to purchase the Existing Notes or an offer to sell securities. The Exchange Offer, the consent solicitation and the solicitation of acceptances of the Prepackaged Plan will only being made pursuant to a confidential Exchange Offer Memorandum, Consent Solicitation Statement, Rights Offering, and Disclosure Statement Soliciting Acceptances of a Prepackaged Plan of Reorganization, which will explain the full terms and conditions of the Exchange Offer, the consent solicitation, the rights offering, and the Prepackaged Plan and will not be made to holders of the Exchange Notes in any jurisdiction in which the making or acceptance thereof would not be in compliance with the securities, blue sky or other laws of such jurisdiction. When and if that material becomes available, holders of the Exchange Notes should read it carefully, as well as any amendments or supplements to that document, because it will contain important information.

The Company has not yet filed with a court the Prepackaged Plan referred to above. In the event the financial restructuring plan is implemented pursuant to the Prepackaged Plan, such restructuring plan is dependent upon a number of factors, including: the filing of petitions for relief under chapter 11 of the U.S. Bankruptcy Code; the filing of the Prepackaged Plan; the approval of a disclosure statement by the U.S. Bankruptcy Court; and the confirmation and consummation of the Prepackaged Plan in accordance with the provisions of the U.S. Bankruptcy Code.

Akin Gump Strauss Hauer & Feld LLP is serving as legal counsel and Stephens Inc. is serving as financial advisor to the Company. Skadden, Arps, Slate, Meagher & Flom LLP is serving as legal counsel to the Supporting Holders.

About Martin Midstream Partners L.P.

Martin Midstream Partners L.P. is a publicly traded limited partnership with a diverse set of operations focused primarily in the United States Gulf Coast region. The Partnership’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

Statements about the Partnership’s outlook and all other 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 current and potential impacts of the COVID-19 pandemic generally, on an industry-specific basis, and on the Company’s specific operations and business, (ii) the Company’s ability to refinance its senior unsecured notes due February 15, 2021 prior to August 19, 2020, (iii) the Company’s pursuit of strategic alternatives, (iv) the effects of the continued volatility of commodity prices and the related macroeconomic and political environment, and (v) other factors, many of which are outside its control, which could cause actual results to differ materially from such statements. While the Partnership 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 the Partnership’s annual and quarterly reports filed from time to time with the Securities and Exchange Commission. The Partnership 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.

Additional information concerning the Partnership is available on the Partnership’s website at www.MMLP.com or by contacting:

Sharon Taylor – Head of Investor Relations

(877) 256-6644