The NHL handed down the punishment on Monday.
Quincey was given a major penalty for elbowing and was ejected from Detroit's 2-1 shootout victory on Sunday. Kopecky was doubled over while leaving the ice following the hit, but he returned to the game.
Detroit leads Nashville and Chicago by a point in the race for the No. 4 seed in the Western Conference. The Red Wings play at St. Louis on Wednesday night.