The suspension was levied after Haynesworth stomped on the head of Dallas center Andre Gurode, who lost his helmet during a five-yard touchdown run by Cowboys running back Julius Jones in the third quarter on Sunday.
An unnecessary roughness penalty was called on Haynesworth and he was ejected from the game.
Gurode needed nearly 30 stitches to close a gash on his forehead and beneath his eye.
"We represent both players here, and it is best for all concerned that we let the suspension stand," said union head Gene Upshaw in a statement. "While Roger has expressed a willingness to meet with Haynesworth and I expect that meeting to take place, there will be no formal hearing where the suspension will be challenged."
Haynesworth has apologized.
Notable deaths of 2014 [PHOTOS]