Mings was also charged with violent conduct by the FA for landing on the Ibrahimovic's head with his studs.
The former Sweden worldwide lashed out on Mings during a coming together in the Cherries' penalty area after the Bournemouth defender appeared to stamp on Ibrahimovic's head.
Manchester United expect Ibrahimovic, 35, to stay at Old Trafford for at least another year, although the Swede is yet to confirm if he will take up the 12-month extension option on his current deal.
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Match referee Kevin Friend did not spot either incident involving Mings and Ibrahimovic.
Ibrahimovic, who has scored 15 Premier League goals this season, will miss Monday's FA Cup trip to Chelsea and the league matches at Middlesbrough and home to West Bromwich Albion.
The FA says it "has submitted a claim that the standard punishment that would otherwise apply for the misconduct committed by the Bournemouth defender is 'clearly insufficient'". He is still available for the Europa League tie against Russia's Rostov on Thursday.
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Mings said after being quizzed on the incident: 'It was a good battle, you know exactly what you are going to get playing against him.
Ibrahimovic retaliated by elbowing Mings in the head, for which he accepted a three-game ban on Tuesday. "I have to think about different matches at the same time". Andrew Surman ended up seeing red for pushing over Ibrahimovic and picking up his second yellow card of the game.
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