The Belgium international appeared to head-butt Stoke City's Ryan Shawcross in Saturday's 1-1 draw between the two sides.
Everton said the player and the club had accepted the charge and Fellaini would now be banned for their league fixtures against West Ham United, Wigan Athletic and Chelsea.
Referee Mark Halsey said he saw two further incidents involving Fellaini and Shawcross, neither of which he deemed to be violent conduct.
"I apologise completely to Ryan Shawcross, my team mates and to our fans at the game," Fellaini said after the match.
"There was a lot of pushing and pulling going on inside the Stoke penalty area and I didn't feel I was getting any protection from the officials.
"Nevertheless I know I shouldn't have done what I did.
"I have also apologised to the manager and the staff. I have no excuses, I was disappointed with the way I was being treated and I lost my temper, which was unprofessional of me."
(Reporting by Toby Davis; editing by Ed Osmond)