The Serbia striker received a three-match ban for the sending off, three for violent conduct and an additional two for “improper, abusive, insulting and threatening” language.
He will also receive a £75,000 fine.
Fulham manager Marco Silva will serve a two-match ban after he was sent off.
In addition to an improper conduct charge for allegedly throwing a water bottle in the direction of the assistant referee, Silva was charged with misconduct for comments he made in a press conference following the FA Cup defeat.
Silva said in a statement he had apologised to Kavanagh and that he “regrets what happened” in the match on 19 March, after he was also charged with abusive behaviour towards match officials.
One game of Mitrovic’s ban has already been served, meaning the forward will be available for Fulham’s last three Premier League games of the season, the first coming at Southampton on 13 May.
Following Mitrovic’s straight red card, the Football Association had said its standard punishment for his dismissal at Old Trafford was “clearly insufficient”.
The 28-year-old denied this but it was upheld by the independent commission, and Mitrovic separately admitted the charge that his behaviour and language after being sent off was improper.
Following the announcement the FA said it would appeal against both sanctions but would wait for the written reasons from the independent commission.
In the FA Cup tie, Fulham’s leading goalscorer Mitrovic had put his side in front against United early in the second half.
But he was dismissed in the 72nd minute after the hosts were awarded a penalty following a Video Assistant Referee (VAR) check that resulted in Willian being sent off for a deliberate handball on the line.
In an apology to team-mates and the club’s supporters, Mitrovic said: “On a personal level, I regret my actions that led to me being sent off.
“I allowed my frustration to get the better of me, and how I reacted was wrong.”
Fulham have also received a £40,000 fine for failing to control their players.
The London club are currently 10th in the Premier League and host West Ham on Saturday.
Source: BBC