Ibrahimovic set up two goals for Robinho and won and converted a penalty for the fourth to leave Milan almost certain of ending their dismal recent record against English opposition.
Kevin-Prince Boateng had fired Milan ahead with a typically emphatic effort in the 15th minute.
Arsenal, who had not previously lost by more than three goals in the Champions League, never got to grips with the nimble footwork of Ibrahimovic, Robinho and Boateng, who pulled their defence all over the place.
The visitors were also at a loss as to how to penetrate the Milan defence where Thiago ilva had an outstanding game. Antonio Nocerino and Luca Antonini were also impressive for the Serie A leaders.
We were never in the game, we were very poor offensively and defensively, and it as shocking to see how were beaten everywhere, Arsenal manager Arsene Wenger told reporters.
It was our worst performance in Europe by far, there was not one moment we were really in the game.
We had to chase the game, open up our game. It was always the same for us, balls over the top, it\'s difficult to analyse. It\'s better not to talk too much and to analyse with a cool head.
AC Milan\'s last three participations in the Champions League have ended in the round of 16 with defeats against English clubs, including Arsenal, but Wenger saw no change of that run continuing.
We don\'t play in dream world....realistically we are out of this competition, he said.
Milan coach Massimiliano Allegri praised his team\'s defence and criticised the attack for not scoring more goals.
We played well as a team, we did not give them any scoring chances, we were very good in defence and especially good when Arsenal had possession, he said.
We could have scored more which is a pity in the Champions League where you have two legs.
The match was played on a shocking pitch at San Siro where both flanks resembled a ploughed field. Around one dozen officials in green uniform spent the halftime interval trying to replace divots and flatten the turf with hoes.
The Serie A champions began with a flourish as Boateng back-heeled the ball to Clarence Seedorf and he shot into the side-netting.
Seedorf limped off after 12 minutes and was replaced by Urby Emanuelson but it made little difference and three minutes later they were ahead.
Nocerino chipped the ball over the Arsenal defence and into the path of Boateng, who chested the ball down and hammered a dipping shot in off the underside of the crossbar.
Nocerino fired over the bar before Ibrahimovic broke down the left, reached the byline and dinked the ball back for Robinho to head the second.
Milan could easily have a third goal before half-time as Boateng broke clear but shot into the side-netting and Antonini poked the ball wide after Ibrahimovic sent him clear.
But it only took four minutes of the second half for them to score again as Ibrahimovic passed the ball behind Robinho but he reacted quickly, got in position and shot into corner.
Arsenal had to wait until the 66th minute for a real chance when Robin van Persie\'s shot on the turn was superbly turned around the post by Christian Abbiati.
Milan were still dominant although their fourth goal came from a highly dubious penalty as Ibrahimovic tumbled over, beginning his fall before any contact had been made by Johan Djourou.
The Swede fired home the resulting penalty to complete the rout.