Nance, who suffered the injury in the Cavaliers' 124-99 loss to the Milwaukee Bucks, has been a significant contributor to the team's solid start (10-14) to the season, excelling on the defensive side.
He is second in the NBA in steals with 1.9 per game. Nance has averaged 9.3 points and 6.8 rebounds in 33.4 minutes a game this season.
He recently missed time with a right wrist sprain.
The loss of Nance further diminishes the Cavaliers' frontcourt, where former All-Star Kevin Love is still out while recovering from a leg injury. Love isn't expected to return before the end of an upcoming five-game Western Conference road trip. The Cavaliers have lost three straight and next play in Phoenix on Monday.