As well as Monday's FA Cup clash, the 35-year-old Ibrahimovic – United's leading scorer this season with 26 goals – will also miss the Premier League matches against Middlesbrough and West Bromwich Albion.
Both Ibrahimovic and Bournemouth defender Tyrone Mings were charged on Monday following two incidents in Saturday's bad-tempered 1-1 Premier League draw.
Mings appeared to deliberately stamp on Ibrahimovic's head as he jumped over him late in the first half at Old Trafford and the Swede seemed to retaliate moments later by elbowing the defender in the head.
Ibrahimovic has now accepted the charge of violent conduct and an immediate three-match ban.
Both players would ordinarily have been facing three-game bans but the FA took the unusual step of saying on Monday that in the case of Mings the standard punishment was “clearly insufficient”.
Bournemouth had until 6pm GMT Tuesday to decide whether to contest the charge against Mings.
On Saturday match referee Kevin Friend spoke to Ibrahimovic, who had already been booked, following his elbow on Mings, but neither player was cautioned.
As a result, the incident was referred to a panel of three former elite referees, who unanimously concluded that both offences merited red cards.
Ibrahimovic denied elbowing Mings on purpose, saying after the game: “I jump up and jump high and he jumps into my elbow. It is not my intention to hurt someone.”
Mings, whose conduct was widely criticized by a number of former players turned football pundits, said he had not intentionally stamped on Ibrahimovic's head.
“I would never do that. That's not in my game,” he said. “Hard and fair is how I like to tackle, but off-the-ball stuff like that isn't part of my game.”
At the very least, Mings now stands to miss league matches against West Ham, Swansea and Southampton.