It was the first time Kane has missed a game in his brief NHL career, having appeared in his first 117 games to date.
The Flames had won five in a row and had earned at least a point their 10 previous games (7-0-3).
Kane, 20, sprained his ankle Tuesday at Detroit and aggravated the injury during Thursday's Winter Classic against the Red Wings.
The reigning Calder Trophy recipient as the league's top rookie has eluded the dreaded sophomore slump, registering 16 goals and a team-best 25 assists in 35 games this season for the Blackhawks, who set a franchise-record nine-game winning streak before dropping both contests to Detroit.
Kane was among three Blackhawks elected Western Conference starters for the 57th NHL All-Star Game on January 25 in Montreal, joining center Jonathan Toews and defenseman Brian Campbell.