Varejao suffered the injury late in the third quarter of Sunday's 98-95 victory against the Los Angeles Lakers. His ankle rolled when he stepped on the foot of the Lakers' Sasha Vujacic.
Varejao left the team in the middle of a three-game West coast road swing, and an evaluation at the Cleveland Clinic by team physician Dr. Richard Parker revealed that his ankle also has bone bruises.
"We're going to need a few guys to step up," forward LeBron James said after Varejao was injured.
The 6-foot-10 inch native of Santa Theresa, Brazil -- a valuable member of the Cavaliers' bench -- is averaging 7.8 points and 8.5 rebounds per game this season.
His injury came at a time when Cleveland had started to right itself in the NBA's Central Division, with eight wins in its past 10 games.