The England striker has mainly had to settle for a wide role this season, on those occasions when he has not been on the substitutes' bench.
Ibrahimovic was among the 20-man squad due to fly to Russia on Tuesday, ahead of their Europa League Round-of-16 tie against FC Rostov on Friday. He is expected to start upfront for that game and will also be available for the second leg at Old Trafford next week.
With 26 goals this season and 20 in his past 23 matches, his importance to United this term has been hard to overstate.
In a statement, the FA said: "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.
"It follows an incident in or around the 44th minute of the game between Manchester United and AFC Bournemouth on Saturday.
"The misconduct was not seen by the match officials at the time, but caught on video."
Ibrahimovic had claimed, after the game, that Mings had jumped into his elbow.
"You can see the TV and the images," he said. "In my situation, I jump up, I jump high, at the same time I protect myself and it's unlucky he jumps into my elbow.
"On many occasions, these things happen and I hope he didn't get injured. What happens on the field stays on the field, I'm not a player who will talk afterwards or attack somebody."
