The clubs were set to play at 2:10 p.m. at Guaranteed Rate Field.
The Guardians said there were multiple positive tests within the organization.
The news comes after Cleveland announced manager Terry Francona tested positive for COVID and would not manage on Wednesday or this weekend’s series against the Twins. Bench coach DeMarlo Hale was set to handle managerial duties.
Major League Baseball will release rescheduling information later.