Ibrahimovic, 35, caught Bournemouth defender Tyrone Mings with his elbow before half-time of United’s 1-1 draw at Old Trafford on Saturday.
The former Paris Saint-Germain forward was stamped on by Mings before he elbowed his opponent, and while both players escaped action from referee Kevin Friend they were charged with violent conduct by the FA on Monday.
Ibrahimovic, who has scored 15 Premier League goals this season, will miss Monday’s FA Cup trip to Chelsea and the league matches at Middlesbrough and home to West Bromwich Albion.
“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.”
Ibrahimovic accepted the violent conduct charge while Mings and Bournemouth have said they will appeal the same charge.