The right-handed Floyd allowed three hits, one run, one walk and struck out one in two innings against the Seattle Mariners before departing. He threw 42 pitches, including 25 for strikes. Floyd was replaced by Hector Santiago.
Floyd, who is 9-9 with a 4.55 ERA in 24 starts this season, will have an MRI on Monday.
Floyd said he began feeling discomfort in the first inning, and it increased in the second inning. He especially felt it when throwing breaking balls. He said it was a similar feeling to when he went on the disabled list in July due to tendinitis in his elbow.
"When I sat down, went back out there (in the second inning), it kind of went back to where it was before when I went on the DL," Floyd said. "I obviously wanted to go back, but it's one of those things that could get worse.
"It was same area, same kind of discomfort. It might have been as intense as it was when I went on the DL. Like I said, I just hope it, I just pray it's something I can bounce back real quick."
White Sox manager Robin Ventura said he wouldn't be surprised if Floyd missed his next start.
Ventura was unsure who would replace him in the rotation. Relievers Philip Humber and Santiago could be possibilities. Both have started games this season, with Humber throwing a perfect game against the Mariners on April 21.