Reyes, who leads the team in RBIs and is second in home runs, was placed on the 10-day injured list before Sunday's game against Minnesota. Cleveland's designated hitter left Saturday's game with the injury, which the team initially called a strained left abdominal muscle.
"We knew he'd be an IL and miss some time," manager Terry Francona said Sunday before the team issued the detailed medical update.
Reyes was injured while fouling off a pitch in the sixth inning. He underwent an MRI on Sunday morning.
Reyes' absence will be a major setback for the Indians. He has 29 RBIs and 11 homers while batting .257 in 40 games. Reyes and third baseman Jose Ramirez have carried Cleveland's offense for most of the season. Reyes hit a two-run homer in the first inning Saturday. He doubled over in pain after taking a swing in the sixth and was replaced during the at-bat by Jordan Luplow.
Infielder Owen Miller, the top hitting prospect in Cleveland's minor league system, was called up from Triple-A Columbus. Miller, 24, was batting .406 in 16 games at Columbus. He started at DH and batted sixth Sunday.
Miller hit two home runs with nine RBIs at Columbus. The right-handed hitter has played all four infield positions and left field.
Catcher Roberto Perez, who had surgery for a broken right thumb earlier this month, was transferred to the 60-day injured list.