The 35-year-old, United's leading scorer this season with 26 goals, will also miss the Premier League matches against Middlesbrough and West Bromwich Albion, dealing a significant blow to United's hopes of snatching a top-four place and a Champions League spot.
However, Ibrahimovic remains available for United's Europa League tie away to Russian side Rostov on Thursday because FA bans do not apply to European matches.
Ibrahimovic and Bournemouth defender Tyrone Mings were charged following two incidents in Saturday's bad-tempered 1-1 league draw.
Both players would ordinarily have been facing three-game bans but the FA took the unusual step of saying Monday that in the case of Mings the standard punishment was "clearly insufficient".
Bournemouth, who were reported to be considering an appeal, have until 1800 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.
Ibrahimovic, who also had a penalty saved by Bournemouth goalkeeper Artur Boruc during the match, 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."
Ibrahimovic has rapidly become a fans' favourite at Old Trafford after linking up again this season with United manager Jose Mourinho, under whom he played at Italian giants Inter Milan, but now the Red Devils must do without him in domestic football until the April 4 visit of Everton at the earliest.
"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."
He added: "If there is reaction (from pundits), there is reaction after. They have time to slow it down and look at it from different angles."
At the very least, Mings stands to miss league matches against West Ham, Swansea and Southampton.
A more severe punishment could also rule him out of the Cherries' fixtures with Liverpool, Chelsea and Tottenham Hotspur.
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