Ibrahimovic was hit with the charge yesterday after the FA took retrospective action against the Manchester United striker.
Mings is likely to be handed more than three games but Bournemouth have said they will contest the charge.
Ibrahimovic though has accepted the ban and will miss games against Chelsea, West Brom and Middlesbrough.
Zlatan Ibrahimovic v Tyrone Mings: Should both players have been sent off?
Mon, March 6, 2017
Zlatan Ibrahimovic and Tyrone Mings have both been charged with alleged violent conduct by the FA for this incident during Manchester United's 1-1 draw with Bournemouth
1 of 13
How long will Tyrone Mings and Zlatan Ibrahimovic be banned for?
Zlatan Ibrahimovic has been banned for three matches after admitting violent conduct
"Zlatan Ibrahimovic will serve a three-match suspension with immediate effect after he admitted an FA charge of violent conduct and accepted the standard penalty," an FA statement said.
"It follows an incident in or around the 44th minute of the game between Manchester United and AFC Bournemouth on Saturday (4 March 2017).
"The misconduct was not seen by the match officials at the time but caught on video."
Get Quotes on Home Insurance