Floyd came out of Sunday's game against Seattle after only two innings because of elbow discomfort.
"Everything structurally seems to be all right, so he still has something in there that they're still checking on, but nothing that would put him out for the rest of the year," White Sox manager Robin Ventura said.
Ventura said Floyd, who joined the team later in the day in Baltimore, will not take his scheduled turn Friday in Detroit. Instead, the White Sox will move Jake Peavy back to that game.
Floyd said that time will tell when he gets back, and he's just going to play everything by ear. He was on the disabled list earlier this summer with tendinitis.
"I want to be here and help the team out as much as possible," Floyd said after Monday's game. "It's very similar, the same kind of deal, the same kind of feel after I [throw] a pitch. It's sore. The same feeling, I would say."
Peavy was originally scheduled to start against the Orioles on Wednesday, and this gives him a few extra days to prepare for that big series.
Ventura said it looks like the Wednesday start will go to Dylan Axelrod, now with Triple-A Charlotte. Axelrod does have a 1-2 record with the White Sox this season. He's made six starts and thrown in 10 games.
"The part that concerns us is that [Floyd has] already had the DL stint before, the same thing, and once he starts talking about it wasn't feeling right, you just don't like that -- to send him back out there or even to have him take his next start. I don't know," Ventura said. "It's just, it concerns you enough when you're dealing with a guy's future and his health and all that."