Carrasco, 32, told Dominican Republic news station CDN 37 he learned of the diagnosis last month. The Indians shut him down in May and placed him on the injured list in early June with an unspecified blood condition.
Leukemia is a form of cancer that affects blood and bone marrow. He did not reveal what type of leukemia he is fighting.
"That's one of the reasons why I'm not playing right now, but I'll be back at the end of July," Carrasco said.
The veteran pitcher did not specify if his return at the end of July would be with the Indians or the start of a rehab assignment.
"We're not putting any timetables," Indians manager Terry Francona said. "I don't think that's fair to anybody. Carlos will make his thoughts known."
Carrasco is 4-6 with a 4.98 ERA this season. He has an 83-66 record and a 3.78 ERA since debuting as a 22-year-old in 2009.
Carrasco has pitched his entire career with the Indians.