Pep Guardiola's side secured a fourth title in five seasons with a dramatic 3-2 comeback victory against Villa at the Etihad Stadium on 23 May.
Thousands of supporters made their way onto the field at the full-time whistle, with smoke flares let off, a goalpost broken and Villa goalkeeper Robin Olsen allegedly attacked.
Greater Manchester Police charged two men over the disorder and are continuing to investigate a number of other offences that took place.
The FA formally charged City on Thursday for failing to control their supporters.
A statement read: "Manchester City FC have been charged with a break of FA Rule E20 following its Premier League fixture against Aston Villa FC on Sunday 22 May 2022.
"It is alleged that after the final whistle of this fixture that Manchester City failed to ensure that its spectators – and all persons purporting to be its supporters or followers – conducted themselves in an orderly fashion and refrained from using threatening and/or violent behaviour whilst encroaching onto the pitch."
City has until 26 August to respond to the charge.