Kane has missed the past two games with a hand injury sustained Jan. 7 against the Tampa Bay Lightning.
His 14 goals are third on the team and he has 25 points in 38 games.
To take his place, the Jets recalled forward Carl Klingberg from the St. John's IceCaps of the American Hockey League.
Klingberg, 22, has 11 goals and seven assists in 33 AHL games. A 2009 second-round pick (No. 34) of the Atlanta Thrashers, Klingberg last played in the NHL in 2011-12 when he had seven shots on goal and four penalty minutes in six games.