After the team's 99-98 come-from-behind win, the Clippers said Butler would be out four to six weeks with a fracture of the fifth metacarpal bone.
Butler had 12 points and two rebounds in 23 minutes, and the Clippers rallied without him. They tied the NBA playoff record for largest deficit overcome at the end of three quarters, when they trailed by 21.
The forward said he thinks he got hurt early in the third quarter when his hand got caught during a pin-down screen in the jersey of Grizzlies forward Rudy Gay, another former Connecticut star. He was able to keep playing but once he went to the bench, he noticed his hand throbbing.
He went to the locker room for an X-ray and returned to the bench.
"I was about to go back in the game, and got the X-ray results," Butler said. "I told Coach I was ready, and he was about to throw me back in the fire."
The veteran forward is one of the few Clippers with playoff experience, though he was injured last year when he was with the NBA champion Dallas Mavericks. A starter, Butler averaged 12 points for the Clippers this season.
"I feel terrible for him," Clippers coach Vinny Del Negro said. "He's been such a pro for us, but injuries are part of it. Other guys are going to have to step up like they did tonight. But replacing Caron right now ... he's been so valuable for us all year. I know the guys feel bad."
Gay was told about Butler's injury after the game.
"People are going to step up, and we're not expecting anything to be easy with Caron or without Caron," Gay said. "We're going to have to go out and play hard."
Information from The Associated Press was used in this report.