Thousands of fans piled on to the pitch at the Etihad Stadium after Pep Guardiola’s team came from two goals down to win 3-2 and clinch the Premier League title.
But there were reports of violence with Villa goalkeeper Robin Olsen assaulted, while numerous visiting supporters have claimed flares, coins and other objects were thrown into their area of the ground.
The Football Association is understood to have launched an investigation and will seek observations from City as well as the police. It has the power to issue disciplinary charges against City should it find the club did not do enough to prevent or deal with the incident.
Greater Manchester Police have so far charged two men, while inquiries into the assault on Olsen remain ongoing.
Phillip Maxwell, 28, of Anzio Row, Knowsley, has been charged with throwing a missile (pyrotechnic) onto the pitch and will appear at Manchester and Salford Magistrates' Court later on Monday.
Paul Colbridge, 37, of Whitegate Drive, Salford, has been charged with going onto the pitch and will appear at the same court on June 7.
City have, meanwhile, launched an investigation and vowed to hand an indefinite ban to the supporter responsible for assaulting Olsen.
Guardiola later personally apologised to Villa and the Swedish goalkeeper for the events which marred his team’s title win.
Sunday’s pitch invasion was the fifth in English football in a week with each drawing a police investigation.
In a statement on Friday, the FA expressed concern at the rise in anti-social behaviour among supporters.
It read: “Football stadiums should always be a safe and enjoyable space for everyone, and these incidents are completely unacceptable and have no place in our game.
It is illegal to enter the pitch area in any stadium and these actions are putting players, fans and people who run the game at great risk. This simply cannot continue and we can confirm that we are investigating all of the incidences.”