The Frenchman sustained the injury after coming off the bench against Fulham on Sunday in United's final game of the Premier League season.
"Anthony Martial is out of Saturday's FA Cup final against Manchester City due to injury," United said in a statement Tuesday.
"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.