Manchester United midfielder Marouane Fellaini and Leicester City defender Robert Huth will each serve three-match bans following their clash in last Sunday's Premier League match at Old Trafford.
The incident occurred during the 21st minute of the 1-1 draw and was not seen by the match officials.
Television replays showed Huth appearing to pull Fellaini's hair before the Belgium international struck him with an elbow.
Both players accepted the charge of violent conduct, although Huth claimed the standard punishment of three matches was "clearly excessive" in his case.
That was rejected at an Independent Regulatory Commission hearing on Thursday and the German centre-back will miss the final two matches of Leicester's triumphant Premier League campaign against Everton and Chelsea, along with the first game of their title defence in August.
Fellaini is ruled out of encounters with Norwich City, West Ham and AFC Bournemouth as United chase a top-four finish, although he will be available for selection when Louis van Gaal's men meet Crystal Palace in the FA Cup final.