Manchester, England:The Football Association announced the punishment after a disciplinary committee had heard the case.
The charge arose out of an incident during Man City's 4-2 victory over Arsenal in the Premier League on Saturday after Van Persie had tackled the striker.
As Van Persie slipped to the turf, Adebayor appeared to kick out and caught him on the side of the head. Van Persie, who needed treatment for a cut, later accused Adebayor of a "malicious stamp."
Man City said Adebayor reluctantly accepted the FA charge. The first game he will miss will be Sunday's match against United followed by a League Cup third-round game against Fulham and another Premier League match against West Ham.
The ban comes with City already without injured strikers Robinho and Roque Santa Cruz and expected to be without Carlos Tevez because of a knee problem.
Adebayor faces the possibility of a further ban arising from another incident in the same game.
The FA has charged him with improper conduct because of his goal celebration. The Togo striker ran the length of the field after scoring against his former club so he could celebrate in front of the Gunners fans.
He has until September 30 to respond to that charge and could suspended or fined.