Jets head coach Paul Maurice made the announcement Monday.
Details of Kane's injury were not made available, but he blocked a shot in Winnipeg's 4-3 overtime win in Minnesota on Saturday and missed practice on Sunday.
It's another blow for the injury-riddled Jets, who are currently without their top four defenceman.
Kane has six goals and nine assists in 26 games with the Jets this season. He had two assists in Saturday's game.
Despite the rash of recent injuries, the Jets are on a roll. They have won four of their last five games heading into Monday's home game against the Wild.