The game at Old Trafford which ended 2-1 in favour of Manchester United saw a major flashpoint in the 67th minute when Antony and Jeffrey Schlupp clashed.
The ensuing melee saw Casemiro grab Will Hughes around the neck which resulted in the Brazilian receiving a straight red card.
Both teams have now been tasked to provide an explanation for the behaviour of their players.
"Manchester United FC and Crystal Palace FC have been charged following a mass confrontation between their players in the 67th minute of the Premier League fixture on Saturday 4 February 2023," a Premier League statement read.
"It's alleged that both clubs failed to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour.
"It's also alleged that Manchester United FC failed to ensure its players refrained from violent behaviour.
"Manchester United FC and Crystal Palace FC have until Monday 13 February 2023 to respond."
Casemiro was handed a three-game ban for his red card.
