Varejao suffered the injury on December 18 against the Toronto Raptors and on Thursday had an operation to repair a small split in his vastus medialis muscle, the Cavaliers said.
"Varejao is resting comfortably and will be admitted overnight. Rehab guidelines will be established today and he is expected to miss the next six to eight weeks," the team said in a statement.
Varejao is the Cavaliers' leading rebounder, averaging 14.4 rebounds a game and he is also their second top scorer averaging 14.1 points per game.
Cleveland are struggling at the bottom of the Eastern Conference's Central Division with a 9-28 record.