The goalie left the game at 19:03 after being hit by the stick of Predators forward Ryan Johansen through his mask. He was replaced by Pavel Francouz, who seconds later made a save on Predators defenseman Mattias Ekholm during a 3-on-2 rush.
Kuemper made nine saves on 10 shots prior to the injury.
"He's doing better and we'll get him further evaluated," Colorado coach Jared Bednar said. "He's got some swelling there, obviously was unable to return, but hopefully he's doing good and is able to get back in the net."
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Francouz, who was making his seventh playoff appearance, finished the game with 18 saves on 20 shots.
"I didn't see what happened initially to Darcy, but I only saw that he was having a lot of pain and I was sure that I'm going in right away," Francouz said. "It's always tough when you see a goalie get hurt, but you have to focus all of your thoughts on the game, on the puck, so that was something I was trying to do. I had huge support from my teammates."
The Avalanche lead the best-of-7 series 3-0. Game 4 will be here Monday (9:30 p.m. ET; ESPN, SN1, TVAS, BSSO, ALT).