Head coach Paul Maurice announced will be out until early February with a lower body injury. The team is also missing defencemen Toby Enstrom, Zach Bogosian, Jacob Trouba and Mark Stuart, who are all currently out of the lineup with injuries.
The 23-year-old Kane, who is making $6 million (USD) this season, has six goals and nine assists in 26 games and has been dropped to the team's third line in recent weeks.
This is his third year in a six-year, $31.5-million contract.
After netting 30 goals and 27 assists in 74 games during the Jets first year back in Winnipeg, 2011-12, Kane hasn't scored more than 19 goals in a season.
He has also come under criticism for his off-ice antics.
Earlier this month, he made headlines for posting a photo on his Instagram account in which he appears to be doing pushups with bundles of U.S. currency on his back, while part of the Las Vegas skyline is visible in the background.
The pushup photo is a callback to his first money shot — a photo from 2012, also taken in Vegas, in which he's shown holding bundles of cash to his ear like its a telephone. That photo angered a lot of people, coming during an NHL lockout in which players were seeking higher salaries.
The pushup photo prompted a Winnipeg woman to ask Kane to step up with his money and donate to those who really need it.
Susan Krepart, a Jets fan who runs the Magnus Hay Formula Drive, a program which raises formula donations for babies through the Winnipeg Harvest food bank, posted a Facebook photo of herself doing push ups with boxes of baby formula on her back.
The caption called on Kane to take some of the cash off of his back and donate it to the formula drive.
Krepart never did hear from the NHLer.