Martin Midstream Partners (MMLP) 8-K Martin Midstream Partners Announces Successful Completion of Exchange Offer and Cash Tender Offer

Exhibit 99.1

MARTIN MIDSTREAM PARTNERS ANNOUNCES SUCCESSFUL COMPLETION OF EXCHANGE OFFER AND CASH TENDER OFFER

KILGORE, Texas, August 12, 2020 (GLOBE NEWSWIRE) — Martin Midstream Partners L.P. (the “Partnership”) and Martin Midstream Finance Corp. (collectively, the “Issuers”) completed their previously announced exchange offer (the “Exchange Offer”) and consent solicitation to certain eligible holders of the Issuers’ 7.25% senior unsecured notes due 2021 (the “Existing Notes”) and separate but related cash tender offer (the “Cash Tender Offer” and, together with the Exchange Offer, the “Offers”) and consent solicitation to certain other holders of the Existing Notes.

Pursuant to the Exchange Offer in exchange for $334,441,000 in aggregate principal amount of Existing Notes, representing approximately 91.76% of the outstanding aggregate principal amount of the Existing Notes, the Issuers (i) paid $41,966,510 in cash, plus $11,854,075.40 accrued and unpaid interest from and including February 15, 2020 until the Settlement Date, (ii) issued $291,969,885 in aggregate principal amount of the Issuers’ 11.50% senior secured second lien notes due 2025 (the “Exchange Notes”), and (iii) pursuant to the rights offering in connection with the Exchange Offer, issued $53,749,957 aggregate principal amount of the Issuers’ 10.00% senior secured 1.5 lien notes due 2024 (the “New Notes”), which amount includes the previously disclosed $3.75 million backstop fee.

Pursuant to the Cash Tender Offer in exchange for $1,225,000 in aggregate principal amount of Existing Notes, representing approximately 0.34% of the outstanding aggregate principal amount of Existing Notes, the Issuers paid $791,250 in cash, plus $43,419.44 of accrued and unpaid interest on such Existing Notes from February 15, 2020 up to, but not including, the Settlement Date.

Ruben Martin, President and Chief Executive Officer of Martin Midstream GP LLC, the general partner of the Partnership said, “We appreciate the continued support of the participating holders and are extremely pleased that over 92% of the holders of our Existing Notes participated in the Offers. With the extension of our debt maturity profile, the Partnership can focus on unlocking value within our existing asset base and continue to strengthen our balance sheet so we are better positioned for future growth opportunities.”

This press release is for information purposes only and is not an offer to purchase, a solicitation of an offer to purchase or a solicitation of consents with respect to any of the Existing Notes. The Offers have been made solely pursuant to the Offering Memorandum or Offer to Purchase, as applicable, and the respective related documents.

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 Partnership’s specific operations and business, (ii) the effects of the continued volatility of commodity prices and the related macroeconomic and political environment, and (iii) 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 “SEC”). 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.

The information in the Partnership’s website is not, and shall not be deemed to be, a part of this notice or incorporated in filings the Partnership makes with the SEC.

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