Barton was sent off for an elbow on City forward Carlos Tevez and, in the aftermath, kneed Sergio Aguero and aimed a head-butt at opposition skipper Vincent Kompany.
The 29-year-old was initially banned for four games after his red card offence, but the FA have suspended him for a further eight after an Independent Regulatory Commission hearing.
Barton had accepted the charge of violent conduct against Aguero, but rejected the same charge against Kompany, but he was found guilty in both counts.
The former Newcastle midfielder also received a fine of £75,000.
The chairman of the Regulatory Commission stated after the hearing: “There are rules of conduct that should be adhered to, and such behaviour tarnishes the image of football in this country, particularly as this match was the pinnacle of the domestic season and watched by millions around the globe.”