Quenneville said he wasn't sure if Versteeg, who suffered the injury during practice Tuesday, would be placed on long-term injured reserve.
"Yeah, kind of frustrating, disappointing for him," Quenneville said. "He was very upset with what happened there. We're disappointed, too, because we really felt that he gives us a lot of versatility and options in our game.
"It looks like he found that stride he was looking for. We want to get him back to that pace when he gets back. We'll get excited again when he gets closer to getting back to our lineup. Certainly he's upset, and it's all part of our game."
Versteeg's injury is not related to the season-ending one that required surgery in 2013 while with the Florida Panthers. He returned at the beginning of the following season only to later say he came back too soon.
Ben Smith is expected to replace Versteeg on the Blackhawks' third line.
Versteeg had 10 goals, 19 assists and was a plus-9 in 63 regular-season games for the Blackhawks last season. His role was reduced in the playoffs, during which he had one goal, two assists and was a minus-5 in 15 games.
He was acquired by the Blackhawks from the Panthers in November 2013.