"The France international strained his hamstring towards the end of Sunday's 2-1 win against Fulham at Old Trafford.
"Assessments have since revealed a muscle tear that rules the 27-year-old out of the Wembley showdown."
Martial scored nine goals in 29 appearances for United this term but was restricted by a series of injuries.
Only 11 of his 21 league appearances have been in the starting line-up, but he had been hoping to be in contention to start at Wembley against City, who are bidding for a treble of Premier League, FA Cup and Champions League.