Blackhawks head team physician Dr. Michael Terry and Dr. Bradley Merk performed the procedure at Northwestern Memorial Hospital.
"Patrick underwent successful surgery today to repair his left clavicle fracture," Terry said in a statement released by the team. "The procedure went very well and we anticipate a full recovery in approximately 12 weeks."
Kane suffered the injury in the first period of Tuesday's 3-2 shootout win over the Florida Panthers and did not return to the game. He was placed on long-term injured reserve, which means he must sit out at least 24 calendar days and 10 regular-season games.
The regular season ends April 11, and the playoffs begin the following week. That means Kane is expected to miss the start of the playoffs and would be out until the Western Conference finals.
Kane was cross checked in the lower back by the Panthers' Alex Petrovic at 7:49 of the first period. The force of the hit knocked Kane to the ice and drove him into the boards. He was slow to get up and was bent over as he skated to the bench. He immediately departed for the locker room.
"Looks like he might miss some time, but we'll know the extent of it tomorrow," Blackhawks coach Joel Quenneville said after the game.
Petrovic, who was given a two-minute minor penalty, is not scheduled to have a disciplinary hearing for the hit, a league source told ESPNChicago.com.
"You get ticked off when the best player in the league gets hit like that," Blackhawks forward Kris Versteeg said. "I can't totally comment because I didn't fully see it. You never want to see that. People pay a lot of money to watch Patrick Kane play. It's never good when he's out of the lineup -- not only for us, but for the league. Hopefully, he's good. We'll see how it goes."
Entering Wednesday's games, Kane was tied for the NHL lead with 64 points and led the Blackhawks with 27 goals and 37 assists. He had not missed a game this season.
The Blackhawks were third in the Central Division with a 36-20-5 record and 77 points going into Wedensday. They trailed the Nashville Predators by 12 points and the St. Louis Blues by three points, and were ahead of the Winnipeg Jets by four points.
"He's 20 to 30 points ahead of the next guy on the team," Versteeg said. (Forward Jonathan Toews is second on the team with 49.) "That's hard to replace that scoring. This team always seems to find ways, so we're just going to have to do that. Dig deep."
The Blackhawks were without Kane for the final 12 regular-season games last season because of a knee injury. He has remained healthy for much of his career and hasn't missed more than 13 games in any regular season in his eight-year career.
"I don't think you can replace the things that he does with the puck, without the puck, the attention that he draws, but one of the strengths of the organization is depth," Blackhawks forward Patrick Sharp said. "You hear it all the time: When a player goes down, you need to step up and collectively fill those shoes. But you guys know as well as I do what kind of player Kaner is."
The Blackhawks recalled top prospect Teuvo Teravainen from the Rockford IceHogs of the AHL on Wednesday.
Teravainen, 20, has two goals and two assists and is a minus-1 in 15 games for the Blackhawks this season. He has nine goals and 16 assists and is a minus-6 in 39 games for the IceHogs.
ESPNChicago.com's Scott Powers, ESPN.com's Pierre LeBrun and The Associated Press contributed to this report.