Rodgers hasn't played since Nov. 4 when he suffered a broken collarbone in his left shoulder and the Packers have gone 1-4-1 in the six games since. Green Bay is 6-6-1 overall, one-half game behind NFC North leaders Detroit and Chicago.
Green Bay Coach Mike McCarthy said Friday that Matt Flynn would be the team's starting quarterback Sunday against Dallas, which at 7-6 and one game back of NFC East-leading Philadelphia, is also fighting for a playoff spot.
"It's been a difficult morning, going through the conversation with Aaron and Dr. McKenzie," said McCarthy. "He feels like he's ready to play. He's had a good week of preparation. He did very little today. He's very disappointed but speaking with Dr. McKenzie, this is the right decision."
Dr. Patrick McKenzie is the Packers' medical director.
Rodgers participated in team workouts this week but Flynn took the plays with the Packers' first-team offense.
Rodgers, the 2011 NFL most valuable player, completed 168-of-251 passes for 2,218 yards and 15 touchdowns while being intercepted four times. Flynn has completed 55-of-88 passes for 615 yards, two touchdowns and two interceptions in three games with Green Bay this season.