Dave Bolland scored two power-play goals to lead the defending Stanley Cup champions to a 4-2 victory over the Flames on Sunday night.
Bryan Bickell and Jonathan Toews also scored power-play goals for Chicago, which went 4 for 9 with the man advantage. It was not immediately clear how long the Blackhawks will be without Kane.
"Kaner probably will be out a little bit. We'll know more [Monday]," Blackhawks coach Joel Quenneville said. "It's nothing real serious."
The Blackhawks killed six of eight Calgary power plays, including four while clinging to a 3-2 lead in the third period.
"The penalty killing got better as we went on," Quenneville said. "Nothing was bigger than the four kills we had in the third."
The Blackhawks were more focused on Kane, who led them last season with 88 points.
Kane sustained a leg injury 46 seconds in and didn't return. He spun and fell awkwardly along the boards while trying to avoid a check by defenseman Cory Sarich. He skated off the ice with assistance and was escorted to Chicago's dressing room. Kane will be re-evaluated on Monday.
The Blackhawks already are without another elite forward, right wing Marian Hossa, who missed his third game because of a lower body injury. He is expected to be sidelined at least another two weeks.
"I don't know what [Kane's injury] is yet," Toews said. "We found a way to win, and we'll have to do that in the future without Kaner.
"We've found a way to play without some or our top players, like Soupy [defenseman Brian Campbell] and Hoss, and know we don't have a choice. We'll do it without Kaner."
Jarome Iginla and Anton Babchuk scored on the power play for the Flames. Babchuk's goal was his first since joining Calgary in a trade from Carolina on Nov. 17.
"It definitely was there for both teams," Iginla said. "We've got to find a way to tie it with that many power plays late.
"After having some momentum on the PP in the first period, we weren't able to get the one more big goal."
Chicago rookie Corey Crawford started for the fourth time in five games and made 24 saves, including some alert ones near the end of the game,
"It came down to just not disciplined hockey and special teams," Calgary coach Brent Sutter said. "It was taking too many penalties and not doing a good job killing them off.
"Your goaltender needs to be your best penalty killer, and he wasn't that."
Chicago held a 3-2 lead after the first period, in which every goal was scored during a power play.
Bickell put the Blackhawks ahead 1-0 at 4:14 when his shot from the slot sailed over Kiprusoff's outstretched glove.
Bolland's connected during a 5-on-3 advantage midway through the period to make it 2-0. Standing at the left edge of the crease, Bolland redirected Toews' cross-ice feed into a wide-open net.
Iginla cut the Flames' deficit in half with 6:54 left when he ripped in a shot from between the circles with Matt Stajan screening Crawford.
Babchuk tied it 2-all with another screened goal just over three minutes later. He beat Crawford with a high shot while Calgary's Olli Jokinen and Chicago's Brent Seabrook were tied up in front of the crease.
Toews batted in a loose puck from a goal-mouth scrum with 2:27 left in the first to restore Chicago's lead.
Following a scoreless second period, the Blackhawks held on in the third. Iginla's shot with 3:40 left struck the right post.
Bolland fired a power-play goal into an empty net to complete the scoring.
Since joining the Blackhawks in 2007 after being chosen No. 1 in the NHL draft, Kane has missed only two games. He sat out twice in January 2009 with an ankle injury. ... Calgary RW Ales Kotalik played his first game of the season after missing 26 because of a knee injury. ... Blackhawks RW Fernando Pisani's upper body injury kept him out for a fourth game.
Information from The Associated Press contributed to this report.