Bickell was injured in Game 2 when he was hit by a skate. He missed Game 3 but his return helped the Blackhawks win three straight to even the series.
"While the surgery was anticipated since the injury occurred, Bryan wanted to play as long as possible before time ran out to complete the procedure appropriately," Blackhawks head physician Dr. Michael Terry said in a statement released by the team. "We anticipate a full recovery in approximately six-to-eight weeks."
The 6-foot-4, 223-pound Bickell scored a goal in Sunday night's 4-3 overtime win and flattened Canucks defenseman Kevin Bieksa with a hard hit. In five games this playoffs, Bickell has two goals and two assists.
Bickell played in 78 games during the regular season with 17 goals and 20 assists.
Tomas Kopecky, who hasn't played since suffering an upper-body injury in Game 1, made the trip to Vancouver.
Information from The Associated Press contributed to this report.