Adebayor cops for three game ban
The FA also confirmed the ban will begin immediately, ruling him out of the Manchester derby on Sunday.
Adebayor had admitted the charge and was dealt with under the FA's fast-track disciplinary system.
A separate charge of improper conduct, brought after the former Gunners player ran the length of the pitch to taunt Gunners fans with a goal celebration, will be considered at a later date.
The FA said in a statement: "A regulatory commission today considered the charge of violent conduct issued against Manchester City's Emmanuel Adebayor under the fast-track disciplinary procedure following an incident with Robin van Persie during their fixture against Arsenal on the 12th September.
"Taking into consideration Mr Adebayor's acceptance of the charge of violent conduct the regulatory commission have ordered that he serve a three-match suspension from all football, commencing Thursday 17th September.
"A separate charge of improper conduct will be considered at a later date."