Brantley was not in the starting lineup Saturday for the fourth straight game and manager Manny Acta said he intends to keep the outfielder out until at least Tuesday.
Acta said that if Brantley does not show improvement, a trip to the disabled list is possible. Brantley has had several tests, including an MRI, and doctors have said the injury is not serious, though the outfielder said it still hurts when he swings a bat.
Cleveland activated outfielder Shin-Soo Choo on Friday and put him in Brantley's leadoff spot. Choo had been out since June 25 with a broken left thumb.
Brantley has hit .270 with seven homers, 13 steals and 44 RBI in 107 games.