Kane was hurt during the first period of Tuesday's game against Florida when he slid hard into the boards after a hit from Panthers defenseman Alex Petrovic. Kane remained down on the ice for a short time and appeared to be favoring his left arm or shoulder before skating to the bench.
The Blackhawks said in a statement that Kane underwent successful surgery to repair a left clavicle fracture.
"The procedure went very well and we anticipate a full recovery in approximately 12 weeks," team doctor Michael Terry said.
The 26-year-old American, whose 64 points is tied with Washington Capital Nicklas Backstrom and Philadelphia Flyer Jakub Voracek for the NHL lead, has not missed any of Chicago's 61 games this season.
A 12-week recovery window would keep Kane out until about May 20, which means he would miss the rest of the season and the beginning of the playoffs, which open on April 15.
Selected first overall by Chicago in the 2007 NHL draft, Kane is a four-time All-Star who won Stanley Cups with the Blackhawks in 2010 and 2013.
He signed an eight-year contract extension with Chicago last July with an annual average value of $10.5 million.
(Reporting by Cameron French in Toronto; Editing by Frank Pingue)