West was off to a blazing start, with 11 points, when he tried to block Rose's layup with 1:36 left in the first quarter. Both players crashed to the court, but while Rose quickly popped up, West stayed down clutching his wrist, which has a nondisplaced fracture. He also had a cut above his left eye that required two stitches.
The Cavaliers began the night with the league's best record. Now, they'll have to make do without a key piece in West, who was fourth on the team at 12.3 points per game.
"They told me I'm going to be out a few weeks with this fracture of my wrist," said West, who is left-handed. "I really don't use my right hand, anyway."
West is scheduled to undergo an MRI on Friday morning.
Information from The Associated Press was used in this report