Fellaini appeared to elbow Huth in the 21st minute of the game at Old Trafford after having his hair pulled by the German defender.
The ban means Huth will miss Leicester's final two fixtures and their first league game of next season.
Fellaini was ruled out United's final three league games of the season but he will be eligible to play in the FA Cup final against Crystal Palace on May 21.
Although both players accepted the charge, Huth's complaint that the three-match suspension would be 'clearly excessive' was rejected following an Independent Regulatory Commission hearing on Thursday, the FA said on its website (www.thefa.com).
Leicester have already won the Premier League title ahead of their final two games of the season while Manchester United are still chasing a top-four finish and a Champions League qualification spot.
Original source: Fellaini, Huth handed three-match ban