Cleveland made the move Friday before opening a three-game series against Minnesota. The American League Central-leading Indians also activated center fielder Tyler Naquin from the disabled list. He had been sidelined with a hamstring injury since May 11.
Erik Gonzalez started the opener at first base in place of Alonso, who is in his first season with Cleveland.
By major league rules, Alonso will have to miss a minimum of three days and a maximum of seven.
Alonso is batting .248 with 11 homers and 37 RBIs in 65 games.
Naquin was hurt running the bases in Kansas City last month. He's batting .333 (25-of-75) with two homers and 11 RBIs in 30 games. He recently appeared in six games on a rehab assignment at Double-A Akron and Triple-A Columbus.