Rodgers suffered a fractured left collarbone in a game against the Chicago Bears on Nov. 10 and has been on the field since.
Green Bay has won its last two outings with Matt Flynn quarterbacking and he will again start on Sunday when the Packers meet the Pittsburgh Steelers. Green Bay is only a half game behind Chicago for the lead in the NFC North.
"I thought Aaron Rodgers did everything he possibly could (to prepare), but this is an organizational decision," Coach Mike McCarthy said. "As an organization, we are not ready for him to play. I'm not going to get into ifs and buts and who made what decision. Matt Flynn is the starter."