Manchester United's Marouane Fellaini and Leicester's Robert Huth have been banned for three games for their clash in Sunday's 1-1 draw at Old Trafford.
Huth pulled the Belgium midfielder's hair, who in turn elbowed the German.
Fellaini, 28, misses United's remaining three league games of the season but is available for the FA Cup final against Crystal Palace at Wembley on 21 May.
Huth, 29, will miss the Premier League champions' final two games and their first league fixture of next season.
The Germany defender will be available to play in the season-opening Community Shield match.
Both players accepted the charge, but Huth argued a three-game ban would be "clearly excessive". The FA's independent regulatory commission disagreed.
The incident was not seen by match officials but was caught on video, with a panel of three former elite referees deciding on the punishment.
Defending the Belgium international, United manager Louis van Gaal said: "It's not in the books that someone has to grab by the hair and then pull it behind - only in sex masochism."
At his news conference on Thursday, he added: "When the FA give Huth a suspension of three matches, then they admit it was a penalty.
"For us it is very disappointing that the referee was not seeing the fact. I think and still believe that Fellaini makes a reaction like a human being but he has to control himself better, that is true. When you grab somebody in his hair, always this situation shall exist."
But Leicester boss Claudio Ranieri said in his news conference on Thursday: "The reaction was worse than the provocation".
Ranieri and his players will be presented with the Premier League trophy on Saturday at their home game with Everton (17:30 BST), with Huth and midfielder Danny Drinkwater both suspended.