Following the game, he said he left the contest with a "painful" knee injury, but that after some tests in the locker room he and team doctors decided he could return to the field for the second half.
Dr. Patrick Jost, a sports medicine specialist at Milwaukee Orthopaedic Group Limited, said it's possible Rodgers could be looking at a ligament sprain.
"He might be fine by next week if he has a minor ligament sprain," Jost said.
But he added the replay of the injury makes him think it's more serious.
"It might have been a meniscal tear based on the way the (Bears' player) fell on him and just where he grabbed his knee," Jost added.
Rodgers failed to walk off the field following the hit.
Jost said it's possible to play on a meniscal tear, but the quarterback's mobility would be severely limited if that proves to be the case.
"He's really good at rolling out, at running out of the pocket and scrambling," Jost said. "That would become more difficult for him."
He said a torn meniscus impacts "people who are twisting, or changing directions. They'll get a sharp pain and it'll keep them from being as fast or as mobile."
He said if Rodgers has a torn meniscus or another serious knee issue, an inability to scramble and escape tacklers could leave the quarterback susceptible to big hits and other injuries.
"That pain and apprehension can change the way an athlete functions," Jost said.
The Green Bay Packers' Twitter account sent out the following Tweet following head coach Mike McCarthy's Monday afternoon press conference: "McCarthy on Aaron Rodgers' status: We're still collecting all the information. I know Aaron wants to play & is driven to play. No decision has been made."