Both teams were involved in a clash after City midfielder Fabian Delph was sent off for a sliding challenge on Max Power in the game that ended 1-0.
The clubs have until Friday to respond to the FA charge.
Meanwhile, Wigan said they would conduct a full investigation after some ugly scenes followed the final whistle
“We appreciate that the vast majority of supporters who ran onto the pitch did so spontaneously to celebrate a famous victory,” the club said in a statement.
“We were disappointed with the action of a minority of supporters who acted in an inappropriate manner.”