Haden was regarded as a game-time decision after he injured his oblique in practice earlier this week, but made the trip to Dallas before being ruled out. Sunday will mark the fifth game Haden has missed this season. He missed four games earlier this year after violating the league's substance abuse policy.
Cornerbacks Dimitri Patterson, running back Brandon Jackson, safety Ray Ventrone, fullback Owen Marecic, defensive tackle Ronnie Cameron and guard Jarrod Shaw will also miss Sunday's contest in Dallas.
Murray was doubtful prior to being ruled out, despite reports that his sprained foot has healed enough for limited activity. He has not played since Week 6.
The Cowboys will also be without cornerback Mike Jenkins, centers Ryan Cook and Phil Costa, defensive end Sean Lissemore, wide receiver Andre Holmes and offensive lineman David Arkin for Sunday's game.