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Rodgers, who suffered a fractured left collarbone Nov. 4 against Chicago, has been practicing on a limited basis but was ruled out by coach Mike McCarthy on Friday.
Rodgers acknowledged earlier in the week that he still has pain in the collarbone.
“He’s very disappointed. He’s frustrated. Speaking with [doctors], it’s the right decision,” McCarthy said.
Matt Flynn will again start in place of Rodgers when the Packers (6-6-1) take on the Cowboys (7-6) in a key game for both teams.
Flynn kept Green Bay in the playoff hunt this past weekend with the team’s first win since Rodgers was injured against the Bears. With three games remaining, the Packers trail the NFC North-leading Bears (7-6) and Detroit Lions (7-6) by a half-game.