Floyd left his start Monday night against the A's after throwing just seven pitches because of soreness behind his right shoulder that he had been experiencing since his previous start against the Twins.
"I'll get it checked out and get a couple MRIs," Floyd said. "I think everything will be fine."
Manager Ozzie Guillen said he won't have Floyd pitch again this season unless he's absolutely certain he is "100 percent" healthy.
"In my mind we've got to go with Plan B," Guillen said. "Right now I think [Tony] Pena's going to be a starter, but I have to wait because I might need somebody in the bullpen the next two days. Maybe Pena's the guy. Maybe we've got to start [Carlos] Torres or whoever's available that day."
Pena came in for Floyd on Monday night and pitched six shutout innings. Earlier in the year he made an emergency start against Kansas City, the only start of his Major League career. He gave up four runs over seven innings.
Floyd said he "really wants to get back out there and pitch," but he also doesn't want to "hurt it any further."
"I'll probably take all precautionary measures," Floyd said. "I don't feel like it's anything serious, but it wasn't getting any better when I was throwing [Monday]. Every pitch it seemed like it was getting worse. We're just treating it and taking it day-by-day."