Mings appeared to deliberately stamp on Ibrahimovic's head as he jumped over him late in the first half at Old Trafford and the Swedish striker seemed to retaliate moments later by elbowing the defender in the head.
Both players would ordinarily face three-game bans, but England's Football Association said in Mings' case the standard punishment was “clearly insufficient”.
“Zlatan Ibrahimovic and Tyrone Mings have both been charged with alleged violent conduct following the Manchester United versus AFC Bournemouth game on Saturday,” the FA said in a statement.
“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.”
“Furthermore, 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 two players have until 6pm on Tuesday to respond to the charges.
Match referee Kevin Friend spoke to Ibrahimovic, who had already been booked, following his elbow on Mings, but neither player was cautioned.
As a result, the incident was referred to a panel of three former elite referees, who unanimously concluded that both offences merited red cards.
Ibrahimovic, United's top scorer with 26 goals, denied deliberately elbowing Mings, saying: “I jump up and jump high and he jumps into my elbow. It is not my intention to hurt someone.”
A three-game ban would see Ibrahimovic miss United's trip to Chelsea in the FA Cup quarter-finals as well as Premier League games with Middlesbrough and West Bromwich Albion.
Mings said he had not intentionally stamped on Ibrahimovic's head.
“I would never do that. That's not in my game,” he said. “Hard and fair is how I like to tackle, but off-the-ball stuff like that isn't part of my game.”
At the very least, Mings stands to miss league matches against West Ham United, Swansea City and Southampton.