The pair were caught by the TV cameras clashing in the penalty area in the first half of Manchester United's 1-1 draw with Leicester on Sunday.
Huth appeared to pull Fellaini's hair, with the United midfielder responding by swinging an elbow into the neck of the German.
A statement from the FA read: " Marouane Fellaini and Robert Huth have both been charged for alleged acts of violent conduct, which were not seen by the match officials but caught on video
"The Manchester United midfielder and Leicester City defender were involved in an incident in the 21st minute of their game on Sunday.
"Both players have until 6pm on Wednesday 4 May 2016 to reply to their charge."
Both men face three-match bans if found guilty.
That would mean Huth missing Saturday's clash with Everton, where Leicester will be presented with the Premier League trophy, and their final game against Chelsea, as well as the opening match of next season.
Fellaini would miss United's last three Premier League games but could return for the FA Cup final against Crystal Palace.
Off-the-ball incidents not seen by the match officials are referred to a panel of three former elite referees, each of whom must deem it a sending-off offence for a charge to follow.
United boss Louis van Gaal was angry about the incident and called for Huth to be banned, saying: ''I expect first that Huth shall be getting a lot (of matches) because I don't think that is normal what he is doing
''Fellaini is reacting like a human being because, when I grab you with your hair and pull it backwards, you shall do also something to me, I believe.''
Source : PA
Source: PA