Rookie left-hander Brian Flynn will start in Cosart's place Thursday night at Pittsburgh.
The Marlins got Cosart last week in a trade with Houston. He made his Miami debut the next day and took the loss against Cincinnati, giving up four runs in 5 1/3 innings Friday. He was 9-7 with a 4.41 ERA with the Astros.
Cosart felt discomfort in his side while playing catch Wednesday and the Marlins decided to have him skip a start. He is tentatively scheduled to pitch next Tuesday against St. Louis.
"We don't feel it's serious but we also want to be cautious," Marlins manager Mike Redmond said.
Flynn was recalled from Triple-A New Orleans on Tuesday when right-hander Jacob Turner was designated for assignment. Flynn pitched once for the Marlins this season, allowing two runs in three innings June 27 against Oakland.