United and Palace players were involved in a brawl in the second half at Old Trafford after Jeffrey Schlupp barged into Antony off the ball.
Both Antony and Schlupp were given yellow cards by referee Andre Marriner but VAR spotted Casemiro grabbing Palace midfielder Will Hughes by the throat during the mele.
After being asked to review the footage on the pitchside monitor, Marriner gave Casemiro a red card, reducing United to 10 men for the final 22 minutes of the game.
The Brazil international has already served a one-game ban for picking up five cards, but he will now be forced to sit out United’s next three Premier League matches after being sent off for violent conduct.
The first game Casemiro will miss is against Leeds United at Old Trafford on Wednesday.
The 30-year-old will then sit out of United’s trip to Elland Road next Sunday.
The final game of Casemiro’s suspension will be against Leicester City on February 19, which means he will be available for United’s Carabao Cup final against Newcastle United on February 26.
United, meanwhile, moved up to third in the Premier League with their 2-1 win over Palace.
Bruno Fernandes’ early penalty gave Erik ten Hag’s side the lead at Old Trafford before Marcus Rashford’s close-range finish doubled their advantage.
Schlupp pulled a goal back for Palace but Patrick Vieira’s side were unable to score an equaliser.