Mings could face an even longer ban because the FA will recommend to a disciplinary commission that his offence deserves a more serious punishment.
Mings and Ibrahimovic have been charged with misconduct by the Football Association and face suspensions after a niggly battle that could have resulted in both receiving red cards.
Both players had protested their innocence following the contest by claiming there was no intent behind their actions, with Mings telling Sky Sports he would "never" purposely stamp on anyone and Ibrahimovic claiming to BBC Sport that Mings jumped "into my elbow".
Ibrahimovic and Mings have until 6 p.m. on Tuesday to reply to their respective charges.
United slumped to yet another draw in the Premier League to start the weekend, failing to put more than one past the previously sieve-like AFC Bournemouth defense - though it was perhaps down more to poor finishing than any actual defensive solidity from the visiting Cherries at Old Trafford.
Explaining the process, the statement continued: "Each referee panel member will review the video footage independently of one another to determine whether they consider it a sending-off offence".
The FA says the incidents "were not seen by the match officials at the time but caught on video".
Both players protested their innocent after the game with Ibrahimovic claiming that Mings "jumped into my elbow". "I'm not someone who attacks someone off the field".
'I knew exactly what kind of game it would be playing up against him and I think we all stood up to the challenge as well. I understand their need for one point in the survival battle and they just defended to make it hard for us ...
That prompted Bournemouth's Andrew Surman to push United's 35-year-old striker over, earning him a second caution of the afternoon, though referee Friend did not brandish a card at either Ibrahimovic or Mings. "For retrospective action to be taken, and an FA charge to follow, the decision of the panel must be unanimous".
"It wasn't intentional", Mings said.
"There was blood everywhere and I remember saying to Bright; Okay, if that's the way you want to play it, then you are having some back".