"It was a tough decision because he's meant so much to us," Rays manager Kevin Cash said. "He tweaked it, but I'm confident we're making the best decision for him and for our club."
Garcia has started 101 games this season, posting a .278 batting average, 17 home runs and 57 RBIs.
"We cannot have Avi go down for a significant period of time," Cash said. "But I think we caught it early enough. We probably won't have him do any swinging for five days and keep our fingers crossed that it's a close to minimum stay."
Cash said he's confident the Rays, who are competing for a wild-card playoff spot, can continue to play well in Garcia's absence.