The incident took place in the 67th minute of the February 4 game, which United won 2-1 at home, as Casemiro was shown a straight red card for grabbing Will Hughes by the throat when both teams clashed following a tackle on Antony.
"It is alleged both clubs failed to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour," the FA said in a statement on Thursday.
"It is also alleged that Manchester United failed to ensure its players refrained from violent behaviour," it added.
The clubs have until February 13 to respond to the charges.