The appeal was heard by Derrick Brooks, the appeals officer assigned to the hearing jointly by the NFL and NFL Players Association.
Gronkowski will miss Monday night's game against the Miami Dolphins.
Gronkowski was penalized on the play but not ejected from the game. It is the first NFL suspension for Gronkowski since he entered the league as a second-round draft choice with the Patriots in 2010.
In remarks to reporters after the game, Gronkowski had apologized to Tre'Davious White for the hit, which came after an interception thrown in his direction. White was on the ground after the play, face-down, when Gronkowski leapt on top of him and put his elbow/forearm into the back of White's head/neck area.
ESPN's Mike Reiss contributed to this report.