The Huyton-born midfielder reacted angrily after receiving a red card for elbowing Carlos Tevez off the ball and kneed Aguero in the thigh following a heated exchange with the Argentine.
After several City players tried to intervene, the 29-year-old then attempted to headbutt captain Vincent Kompany as he was dragged from the field.
His former City team-mate, Micah Richards, attempted to calm Barton but that did not stop him almost clashing with substitute Mario Balotelli before entering the tunnel.
An FA statement read: "The FA has today [Monday 14 May] charged Queens Park Rangers midfielder Joey Barton in relation to two acts of alleged violent conduct during Sunday’s match against Manchester City at the Etihad Stadium.
"Following the player’s dismissal in the 54th minute of the fixture, there followed two incidents involving Manchester City’s Sergio Aguero and Vincent Kompany.
"As Barton had already been dismissed, both of these incidents fell outside of the jurisdiction of the referee.
"Barton has until 6pm on Tuesday 15 May to respond to the charges."
Following the match, the former City man took to Twitter to insist his actions were an attempt to goad an opposition player into being sent off.