Casey will begin serving his suspension immediately.
Outfielder Coco Crisp, meanwhile, had his hearing Monday in Boston and is awaiting word from Major League Baseball on whether his seven-game suspension will be reduced.
In all, eight players from the Red Sox and Rays were suspended a total of 38 games following the June 5 brawl. The fight started when Crisp rushed the mound after being hit in the right hip by a pitch from James Shields.
Tempers had carried over from the previous night, when the Rays complained about Crisp's hard slide into second baseman Akinori Iwamura on a steal attempt.