Brian Flynn will make the start for Miami in the series finale at PNC Park.
Cosart's ailment isn't believed to be serious, and it is not landing him on the disabled list. On Tuesday and Wednesday, Cosart played catch and said he is improving.
"If this was the World Series and I had to pitch, I'd pitch," Cosart said. "It's more on the precautionary side. It's more tight. It's not a sharp pain. It's nothing like that. It's just kind of uncomfortable. I don't want to be uncomfortable, and they don't want me to be uncomfortable. I've got a bullpen [session] on Saturday, and I'll be ready to go."
Manager Mike Redmond said the club anticipates Cosart rejoining the rotation on Tuesday against the Cardinals at Marlins Park.
"It's unfortunate, but it looks like it's not going to be a long-term deal," Redmond said.
The Marlins acquired Cosart from the Astros on July 31, and he took the mound in Miami the next day against the Reds. In 5 1/3 innings, the righty was charged with four runs -- three of which scored after he left the game.
Switching from the American League to the National League means Cosart now gets to bat. He actually did his job at the plate, collecting his infield single and dropping down a sacrifice bunt.
But on his hit, he felt soreness in his left side after either the swing or sprinting to first base.
"Most likely on the swing, but I don't really know," Cosart said.
"It flared up on him," Redmond said. "It will keep him from making that start."
While Miami tabbed Flynn for Thursday, the club hasn't announced Saturday's starter yet. But it is expected to be veteran Brad Penny, who is currently at Triple-A New Orleans.
The Marlins' rotation already is without Henderson Alvarez, who is on the DL with right shoulder inflammation. Alvarez played catch on Wednesday and he is progressing nicely. The expectation is the All-Star will be reinstated on Aug. 14, the first day he is eligible to return. Miami faces Arizona that day at Marlins Park.
Flynn was called up from New Orleans on Tuesday when Jacob Turner was designated for assignment. Turner on Wednesday was claimed off waivers by the Cubs.
The initial plan was for Flynn to be used in long relief, but now he will make his first start for Miami this season. His lone outing at the big league level this year was three innings of relief against the A's on June 27.