Sergio Aguero: Manchester City striker avoids punishment for fan altercation
Television footage appeared to show Aguero pushing a supporter and he later claimed he was spat and sworn at.
Both clubs have been charged by the FA for failing to control their players after Fabian Delph was sent-off.
But no individual players or staff will face any disciplinary action.
Delph's first-half red card led to a heated argument between City boss Pep Guardiola and opposite number Paul Cook in the tunnel at the break, but the FA said "no misconduct took place".
The clubs have until 18:00 GMT on Friday to respond to the charges, while Aguero has been "reminded of his responsibilities".
Wigan and City have also been asked to provide their observations to the FA by Monday, after crowd trouble at the end of the game, which saw fans invade the pitch.
Some supporters at the DW Stadium ripped out advertising boards and threw them towards police.
Police say two arrests were made on suspicion of affray after an incident outside the ground.
Chairman David Sharpe says Wigan will work with the FA and police to review the pitch invasion.
Will Grigg scored the winner as League One Wigan beat City 1-0 and ended their hopes of winning a Quadruple of the Premier League, FA Cup, League Cup and Champions League.
It is understood Aguero is considering legal action against a fan who confronted him.