Rays manager Joe Maddon said he hasn't met with the training staff to hear their opinion on any possible injury, though.
Maddon added the plan is for Price to do his normal throwing session leading up to his next start, but that there was no way he would have let him finish Friday's game.
"He could have fought all that he wanted, but once I hear 'back,' he's out," Maddon said. "There's so many things it could be, but when you say 'back,' I don't even want him to throw a couple pitches to find out. That's the part for me that becomes non negotiable at that point."
If Price is unable to pitch in his next start, which is scheduled for July 4 against the Yankees, a likely candidate to be called up would be Chris Archer, who made two starts while Jeremy Hellickson was on the disabled list.
Archer is scheduled to pitch for Triple-A Durham on Friday, but Maddon said the Rays will know if they need him to start in Price's place before he takes the mound.
"I just want to let it play all out," Maddon said.
A bigger concern, though, is if Price is able to make the start but needs to be pulled early because of the injury.
"If we get to the point where David's gonna pitch or you expect him to pitch, it's more of a how do you work the rest of the game if he's not able to go through the second or third inning," Maddon said.