Adebayor said immediately after the match that he was trying to kick the ball, but Van Persie subsequently claimed his former team-mate had deliberately set out to injure him in a "malicious" manner.
City manager Mark Hughes is now facing a striker crisis for Sunday's derby, with Craig Bellamy the only one of the club's senior strikers likely to be available.
Robinho, Roque Santa Cruz and Benjani Mwaruwari are all injured and Carlos Tevez is rated extremely doubtful to face his old club.
On top of the trip to Old Trafford, Adebayor will also sit out the Carling Cup tie with Fulham next Wednesday and a Premier League meeting with West Ham on 28 September.
City have two more weeks to consider the improper conduct charge relating to Adebayor's goal celebration in front of the visiting Arsenal fans after scoring City's third goal.
After the match it emerged that a steward needed hospital treatment after being hit by a flying object following Adebayor's celebrations.
The striker, who apologised for his actions after the match, said emotions "took over me" and that it was "silly" to run up to the fans, but claimed he had been insulted for the whole game.
Premier League chief executive Richard Scudamore said on Monday that these instances "don't do the image of the league or football in general any good".
Although Manchester United's Gary Neville was fined £5,000 for a similar offence, when he celebrated in front of Liverpool fans at Old Trafford in 2003, the FA does have the power to suspend players for such behaviour.
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