He will miss Thursday's game against the New Orleans Saints.
On Monday, the NFL announced Hill would be suspended two games for punching Las Vegas Raiders guard John Simpson after the Cowboys' overtime loss on Thanksgiving Day. He can return to the club in time to play Dec. 12 against the Washington Football Team.
Derrick Brooks heard Hill's appeal on Tuesday and agreed to cut the penalty in half; however, the Cowboys were hoping to have Hill against New Orleans. With a Thursday game, the timing of the suspension's announcement was odd considering the Cowboys were well into their game preparation.
Hill's suspension was issued by NFL vice president of football operations Jon Runyan for violations of unnecessary roughness and unsportsmanlike conduct rules.
"After the Las Vegas Raiders-Dallas Cowboys game on November 25, you engaged in conduct that this office considers unnecessary roughness and displays a lack of sportsmanship. Specifically, as both teams were shaking hands, you waited more than 50 seconds for your opponent at the 50-yard line. When you located him, you then walked toward him in the opposite direction of your locker room. You both engaged in a verbal chest-to-chest confrontation which you escalated by throwing an open hand punch to his facemask, forcible enough to cause your opponent's helmet to come off," Runyan wrote in the letter to Hill.
Cowboys coach Mike McCarthy has not had a chance to talk to Hill in person since entering COVID protocols on Monday, but will when he is cleared.
"I know his coaches have spoken to him," McCarthy said earlier Tuesday. "He's obviously apologized for it, really the next day. I didn't find out about it until clearly after the game, quite some time. He's acknowledged the fact that what he did was not right. We'll deal with that and move ahead accordingly."
Hill has played in the past three games after opening the season on the physically unable to perform list because of a serious knee injury. He has been credited with eight tackles and four quarterback pressures. The suspension will cost him $52,137.