They were cut for both performance and “locker room” reasons, reports NFL.com’s Ian Rapoport.
Michael has played in only five games this season after Dallas acquired him from Seattle. White has played in seven games, but was listed as inactive the last two weeks.
The Cowboys have lost seven games in a row since an injury to quarterback Tony Romo.
Dallas has had issues with player behavior this season. In late October, defensive end Greg Hardy was caught on video yelling at teammates and shoving a special teams coach during a loss to the New York Giants.
Michael ran for 51 yards on 15 carries in his time on the field. White recorded six tackles before being released.
Dallas also released quarterback Brandon Weeden on Tuesday.