Format: 

Lastname, Firstname. "Title of Press Release." Title of Website, Publisher, Day Month Year. Press Release. Database Name or Title of Non-Publisher Website, URL. Accessed Day Month Year.

Lastname, Firstname. "Title of Press Release." Title of Website, Publisher, Day Month Year, URL or DOI (when accessed from the publisher's website). Accessed Day Month Year. Press Release.

Lastname, Firstname. "Title of Press Release." Title of Website, Publisher, Day Month Year. Press Release.

Examples: 

"Bridgestone Begins Producing Natural Rubber in Mesa, Arizona." Bridgestone Americas, Inc., 22 Sep. 2014, bridgestoneamericas.com/en/newsroom/press-releases/2014/bridgestone-begins-producing-natural-rubber-in-mesa--arizona. Accessed 12 Dec. 2008. Press Release.

In-text: ("Bridgestone")

Rosen, Ellen. "Princeton Review Names RIT Among Best Colleges." University News, Rochester Institute of Technology, 4 Aug. 2015, https://www.rit.edu/news/story.php?id=52779. Accessed 12 Dec. 2008. Press Release.

In-text: (Rosen)

Notes: 

Press release titles should be wrapped in quotation marks since they are part of the larger body of content published by a company or organization (MLA 25). The name of the company or organization can be used as the author when the individual author is not known, but if that entity is also the publisher of the press release (as is often the case), the author should be omitted (MLA 25). Similarly, if the title of the website is more or less the same as the name of the publisher, you can also omit the publisher (see first example) (MLA 42). Provide the direct URL for the item, but omit the http:// or https:// (MLA 110); an access date should also be provided for web sources (MLA 53). Since a press release is a less traditional source and is not explicitly covered by the MLA manual, you should provide a brief descriptive label (i.e. Press Release) at the end of the citation (MLA 52). Do not include page numbers or paragraph numbers for your in-text citation unless they are explicitly listed on the press release (MLA 56).

Source:
MLA - p. 44