The Rays made the announcement about the AL wins leader before their game Friday night against Texas.
"We feel confident that it's not a major situation," Tampa Bay executive vice president of baseball operations Andrew Friedman said. "It's something that we wanted to get in front of and make sure that it wouldn't become one."
Right-hander Chris Archer was recalled from Double-A Montgomery to replace Price (17-5), who could miss only one start.
"It's the first time I've ever had soreness in my shoulder like that so I'm just going to take it slow," Price said. "I played catch today, felt good, so I'm just looking forward to (throwing again) Sunday or Monday and making my next start. It's a good time for me to miss a start and get that extra rest, then come back and be ready to throw."
Rays manager Joe Maddon expects Price will start during a series at the New York Yankees that begins next Friday.