The Hawks' last regular-season game is April 10.
"We hope to have him back before the end of the regular season," Quenneville said. "He feels better the last couple of days, so we'll see his progress over the next little bit."
Sharp had a knee-on-knee collision with Phoenix's Rostislav Klesla on Sunday. Sharp had to be helped from the ice and was favoring the knee, though Quenneville said only that it was a "lower-body injury."
"It could have been worse for sure," Quenneville said. "It's not long term, but right now long term is basically how we're looking at it."
Sharp has a career-high 68 points this season -- 34 goals and 34 assists.
"It always hurts to be missing one of your top players, especially your top goal scorer," Toews said. "Sharpie has been great for us in the last couple of months while we've been chasing a playoff spot."
Meanwhile, Dave Bolland's return remains uncertain. He took a shot to the head on March 9.
Brian Campbell, who has a left foot injury, hopes to return Wednesday against the Panthers.
Jesse Rogers covers the Blackhawks for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.