They promoted quarterback Joe Callahan from the practice squad on Saturday, giving them three quarterbacks on the active roster.
Callahan would back up Brett Hundley if anything happened to Rodgers.
The Packers waived linebacker Carl Bradford to make room for Callahan.
The undrafted rookie was on the Packers' active roster for the first five weeks of the season. He was claimed off waivers by the New Orleans Saints and also spent time on the Cleveland Browns' active roster before coming back to Green Bay on the practice squad a little more than two weeks ago.
Rodgers was listed as questionable for Sunday's game against the Bears at Soldier Field. He was injured on the third play from scrimmage in last Sunday's win over the Seahawks. He played into the fourth quarter and with the game out of reach, Hundley replaced him.
He did not practice on either Wednesday or Thursday, but coach Mike McCarthy said Friday that he hoped Rodgers would take a few reps during Saturday's light workout before the team traveled to Chicago. The Packers did not update their report on Saturday, meaning Rodgers' status has not changed.