Mings landed on the United forward's head with his studs and Ibrahimovic caught Mings in the face with his elbow soon afterwards during the teams' 1-1 Premier League draw at Old Trafford on Saturday.
"The players were involved in two separate incidents in or around the 44th minute which were not seen by the match officials at the time but caught on video," the FA said in a statement.
The players have until 1800 GMT on Tuesday to reply to the charge and face minimum three-match bans if found guilty.
Swede Ibrahimovic, who has 26 scored goals in all competitions for United this season, could miss the FA Cup quarter-final trip to Chelsea next Monday.
Mings could face an increased ban for his offence.
"The FA has submitted a claim that the standard punishment that would otherwise apply for the misconduct committed by the Bournemouth defender is 'clearly insufficient'," the FA said.
(Reporting by Mark Gleeson; Editing by Ed Osmond)
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