Varejao suffered the injury during the Cavaliers' 113-99 defeat to the Toronto Raptors Dec 18, reports Xinhua.
He will undergo surgery on Thursday before being sidelined for six to eight weeks, according to team doctor Richard Steadman.
Cavaliers coach Byron Scott says he expects the 30-year-old could return before the end of the season.
"I may just go up to him and give him a big hug and tell him it's going to be OK," Scott said.
After an injury-ravaged two seasons, Varejao was quite on form this season, averaging 14.1 points and 14.4 rebounds a game.
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Varejao missed 51 games in 2011 with a torn ligament in his foot and 41 games last season after breaking his wrist.
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