Hossa left Wednesday's game with an apparent arm or shoulder injury in the second period after falling near a corner on a Blackhawks power play. Officially, the team is deeming it an "upper body injury."
"It's not of a serious nature," Quenneville said.
The Blackhawks were still discussing who they might recall from Rockford of the AHL to replace Hossa on the roster.
"[Hossa] has been great for us picking up a lot of the slack on offense and scoring," Jonathan Toews said Thursday on "The Afternoon Saloon" on ESPN 1000. "All your veterans have to make up for that void now that we hope he will be back sooner than later, but you never know.
"It's something that, especially early in the season, you don't want him to push it and come back too quick. I think it will be a good opportunity for some of our other guys to get a little ice time."
Hossa was off to a quick start this season after missing the beginning of last year with a shoulder injury. He is second on the team with 11 points.
Jesse Rogers covers the Blackhawks for ESPNChicago.com and ESPN 1000.