Hossa suffered the injury during the first period of Saturday's game against the Pittsburgh Penguins at Soldier Field.
"There's going to be some quality ice time shared amongst the guys," Quenneville said. "I thought [Brandon Saad] did a real good job being put up on that line there as the game progressed the other day. We'll probably put him there. We'll get Peter [Regin] back in the lineup, and we could always put [Andrew] Shaw on the right. We'll see what happens."
Hossa has had a variety of injuries the past three seasons. He suffered a severe head injury in the playoffs in 2012. He dealt with a back injury during the Stanley Cup finals last season and missed all of the team's preseason games this season due to it. He also missed three games in November because of an undisclosed lower-body injury.
He has 24 goals, 26 assists and plus-25 rating in 57 games this season.
Quenneville wasn't sure whether the Blackhawks would recall any players from the Rockford IceHogs of the AHL.