Mings was also charged with violent conduct by the Football Association, but Bournemouth said they will appeal against the defender's charge.
Ibrahimovic had fallen after a tackle and Mings's right boot caught the Swede on the side of the head.
He will also sit out his side's Premier League matches with both Southampton and West Brom.
The FA said in a statement: "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".
"It follows an incident in or around the 44th minute of the game between Manchester United and AFC Bournemouth on Saturday (4 March 2017)".
Ibrahimovic has been a key player for Manchester United in front of goal this season and has already notched up 26, proving the critics who had said that he was just coming to the Premier League for the money and would struggle with the pace of the game wrong. Ibrahimovic was initially said to be set for a move to the MLS, after his contract with PSG expired, but chose to join Manchester United instead after getting a call Jose Mourinho. There will be things highlighted more than others, but I enjoyed it'.
Ibrahimovic faces the possibility of a three-match ban and could miss United's FA Cup trip to Chelsea. "I have to think about different matches at the same time".
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