Almonte was placed on the 10-day disabled list on Tuesday. He underwent an MRI, which revealed the nature of his injury.
The Indians called up top outfield prospect Bradley Zimmer on Tuesday to help replenish their outfield. After going hitless in his debut Tuesday, Zimmer had his first major league hit and later added a home run in the Indians' 7-4 loss to the Tampa Bay Rays on Wednesday.
Zimmer, 24, was Cleveland's first-round draft selection in 2014. He was off to a solid start this season in Columbus, batting .294 with five home runs, nine stolen bases and a .532 slugging percentage in 33 games. He was rated as the Indians' third-best prospect earlier this year by ESPN's Keith Law.
Almonte, who has made 22 starts in right field and four in center field this season, is hitting .221 with one home run and six RBIs this season.