Kane's injury came the morning after the Jets lost, 3-0, to the Montreal Canadiens at MTS Centre. The Jets did not reveal Kane's status for the team's next game Friday night against the St. Louis Blues.
Kane appeared to sustain the injury after getting caught up with fellow forward Anthony Peluso.
"He got a tweak in practice and he'll get assessed sometime today. We'll go from there," Jets coach Claude Noel said. "[He's] day-to-day right now."
In seven games this season, the 22-year-old is tied for the team lead with three goals.
Winnipeg is in the midst of a season-long six-game homestand and has scored four goals in the first three games, going 1-2-0 in the process.
Forwards Bryan Little and Jim Slater missed practice for maintenance days. But regardless of who is available for the team's next game, Noel made it clear that his players needed to improve over the course of the current homestand.
"I don't think anybody is happy with the way we're playing. The level of joy is low," Noel said. "I think that we need to change. If players can't seem to change the way things go, then things will change around them. It's that simple."