Chris Thorburn will take Kane's place on the Jets' second line with Blake Wheeler and rookie center Mark Scheifele. Wheeler, who leads the team with 21 goals, sat out the morning skate Tuesday but will play against the Predators.
James Wright will take Thorburn's spot on the Jets' fourth line.
"It's a really unfortunate setback for [Kane]. For our team but certainly for him because I liked the way he was coming and going and we're going to miss him," coach Paul Maurice said of Kane's injury.
A run of six wins in seven games for the Jets since Maurice took over has pushed them one point past the Predators for sixth place in the Central Division.
The Jets have allowed 13 goals in Maurice's seven games since replacing Claude Noel, and captain Andrew Ladd credits the new bench presence with rebuilding both the Jets' confidence and its defensive structure.
"I think the things [Maurice] has implemented have made us quicker defensively," Ladd said. "We're on the puck and not giving teams time and space.
"We're playing with confidence right now. I think that we feel that we should win every game. We know what's ahead of us and know that we'll have to string some wins together but I think that's an exciting challenge for this group, especially with the way we're playing."
The Predators are winding down a four-game tour through Western Canada. They're 1-1-1 on the trip but the Edmonton Oilers dealt them a 5-1 loss Sunday at Rexall Place.
"This will be a tough test," Predators coach Barry Trotz said. "I said to our guys this building will probably have a lot of playoff feel. They're passionate fans and they're excited by where the [Jets] are lately. So don't be intimidated by it. It's a good feeling. It will be a fun game and I hope our guys are up for the challenge."
Predators forward Colin Wilson did not participate in the morning skate at MTS Centre but will play against Winnipeg. Center Matt Cullen (upper body) is questionable after missing the game Sunday while left wing Viktor Stalberg (upper body) will miss his second consecutive game.
The Predators recalled rookie center Colton Sissons from the Milwaukee Admirals, their American Hockey League affiliate, on Monday. Sissons leads the Admirals with 16 goals and 28 points and was named to the 2014 AHL All-Star Team. Trotz expects Sissons will make his NHL debut and play on the Predators' penalty kill.
Here are the probable lineups for the Predators and Jets:
Scratched: Mattias Ekholm