The team announced Wednesday that Carrasco is stepping away from the team to explore treatment and recovery options after feeling lethargic for the last few weeks.
The club said it do not know when Carrasco will rejoin the team, but he is expected back this season.
Carrasco has struggled lately for the Indians, losing three straight games to drop his record to 4-6 with a 4.98 ERA.
The 32-year-old signed a four-year contract extension in December 2018 that will keep him in Cleveland until 2022 with an option for 2023.
Carrasco was to start Wednesday's home game with the first-place Minnesota Twins. Cleveland trails Minnesota by 10 1/2 games in the American League Central.