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 incident was not seen by the match officials but the charge was brought after a panel of three former elite referees viewed the video evidence and determined the players were guilty of a sending-off offence.
Fellaini and Huth are facing three-match suspensions, the standard punishment for violent conduct.
Both players have until Wednesday to reply to the charge, the FA said on its website (www.thefa.com).
Leicester City have already been crowned Premier League champions ahead of their final two games of the season.
Manchester United, who are still chasing fourth place and a Champions League qualification spot, have three league games remaining.
A three-match ban would leave Fellaini eligible to play in the FA Cup final against Crystal Palace on May 21.
Original source: Fellaini, Huth charged with violent conduct