Rodgers will miss his seventh consecutive game because of the injury, leaving backup Matt Flynn under center on Sunday when the Packers host the Pittsburgh Steelers in a game that has play-off implications for both teams.
"As an organisation we feel we are not ready for him to play. He is not medically cleared," Packers head coach Mike McCarthy said.
"Everything has been explained, but he obviously wants to play. The kid has played with injuries. He's a tough guy. He's done everything he possibly could to try to get back on the field."
Green Bay can claim their third consecutive NFC North title and a play-off berth by beating Pittsburgh on Sunday and the division-leading Chicago Bears (8-6) on December 29.
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