Green Bay's winning streak ended at four games but the larger concern for the Packers is the health of Rodgers, who injured his non-throwing left shoulder when he was sacked on the first series by Shea McClellin.
Rodgers tried a few throws with backup Seneca Wallace but, after being examined by medical staff, ran into the locker room. He returned to the sidelines wearing sweats midway through the third quarter.
"They want to run more tests," Coach Mike McCarthy said. "They don't have an exact diagnosis. We'll have more information, probably tomorrow."
Alshon Jeffery had five catches for 60 yards, including a six-yard reception for the go-ahead touchdown at the end of the third quarter. Brandon Marshall, largely shut down in two games against Green Bay last year, had seven catches for 107 yards and a touchdown. Matt Forte ran for 125 yards and a touchdown and had 54 yards receiving.
The victory pulls the Bears into a three-way tie for first place in the NFC North with Green Bay and Detroit.
The loss spoiled another big night by Green Bay rookie Eddie Lacy, who ran for 150 yards and a touchdown.
McCown completed 22 of 41 passes for 272 yards. He mixed his passes effectively to Marshall, Jeffery and Forte, and Forte ran roughshod on the Green Bay defense.
Wallace hadn't played since 2011 and the rust was evident. He had a pass intercepted by Julius Peppers on his first series.
The Packers had second and goal from the Bears five late in the third quarter and were forced to settle for Mason Crosby's 23-yard field goal after Wallace overthrew James Jones and Andrew Quarless. Green Bay would get no further than the Bears 39 the rest of the game.
Wallace finished 11 for 19 for 114 yards.
"Seneca, he needs to perform better and he'll definitely do that with a week of practice," McCarthy said.