After the game, 23-year-old Mings denied his action was deliberate, saying: "I would never do that. That’s not in my game. Hard and fair is how I like to tackle."
While Ibrahimovic said that his elbow was also not intended to come into contact with his opponent’s face, adding that Mings had jumped into his arm.
However, the FA have charged both players, who have until 6pm on Tuesday 7 March to appeal.
And Mings could be in for an extended ban if found guilty, with an official statement from the governing body saying:
" 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’."
A possible three-game ban for Ibrahimovic would rule him out for the rest of March, with an FA Cup quarter-final against Chelsea and Premier League meetings with Middlesbrough and West Brom next up.
If Mings is handed an extended ban it would rule him out until mid-April, with the Cherries currently having 11 games remaining this season.
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