Alonso returned Monday after missing a weekend series against Minnesota. Alonso is batting .248 with 11 homers and 37 RBIs in 65 games for Cleveland, which signed him as a free agent in December.
To make room for Alonso, the team optioned outfielder Greg Allen to Triple-A Columbus.
The Indians also signed reliever Marc Rzepczynski to a minor league contract and assigned him to the Clippers. The left-hander previously pitched for the Indians from 2013-15, appearing in 145 games. He pitched in a career-high 73 games for Cleveland in 2014.
He pitched last season with Seattle and two months in 2018 with the Mariners before being designated for assignment on June 1. He has appeared in 501 career major league games.
Also, outfielder Melky Cabrera cleared waivers and elected free agency. The team designated him for assignment last week.