The veteran Rinne had 15 saves on 18 shots before leaving Friday night's 5-3 win over the Calgary Flames with just under 15 minutes left in the third period. He earlier had collided with teammate Kevin Fiala when Flames forward Sam Bennett tied the game at 3 at 2:20 of the third period.
Juuse Saros replaced him and stopped all nine shots he faced to pick up the win.
Rinne has a 3-1-0 record, a 2.10 goals-against average and a .929 save percentage in five games this season. He won the Vezina Trophy as the NHL's top goalie last season.
The Predators did not say how long he will be out. The team recalled goalie Miroslav Svoboda from ECHL-Atlanta.
"We never want to see that happen to him. He's such a big part of our team and been playing really well to start the year here, following up from last year," Predators coach Peter Laviolette said. "But this is part of the game, and it happens to all teams, so it's happening to us right now."
Nashville plays at Edmonton on Saturday night.
"We'll have to deal with it tonight and until we get back," Laviolette said. "But there's a lot of confidence in [Saros] and the way he plays the game and a great opportunity for him. ... [Saros] has given us no reason to think he can't handle this. He's been outstanding the last few years every opportunity he got. ... That's what he's done since he's been here, and that's why there's a lot of confidence from the players that play in front of him."