Rodgers is said to have suffered a small break in his collarbone on the opening series of Monday night’s 27-20 loss to Chicago when he landed on his left (non-throwing) shoulder after Packers defensive end Shea McClellin sacked him.
NFL.com reported no definitive timetable for the 2011 league MVP exists but Rodgers “likely” would return in time for the playoffs.
Other reports suggested Rodgers could be out of action three weeks.
Tenth in the league in passing yardage with 2,218, Rodgers will have further testing on Tuesday.
His loss is devastating for a Packers team that is in a three-way tie for first place atop the NFC North. Green Bay, Detroit and Chicago each have 5-3 records.
After being sacked, Rodgers took a few warmup throws with backup Seneca Wallace but, following examination by medical staff, ran to the Green Bay locker room.
The Packers have been hit hard by injuries, with Pro Bowl linebacker Clay Matthews (thumb), wide receiver Randall Cobb (fibula) and tight end Jermichael Finley (neck) sitting out Monday’s game.