Martial came on as a second-half substitute at Old Trafford on Sunday, playing the last 23 minutes.
After reporting the injury after the game, assessments done by United medical staff on Monday and Tuesday revealed a muscle tear and the 27-year-old will now not be part of Erik ten Hag's squad against City.
A statement issued by the club on Tuesday read: "Anthony Martial is out of Saturday's Emirates FA Cup final against Manchester City due to injury.
"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 has struggled with injury all season and has been restricted to 29 appearances in all competitions, scoring nine goals.
His latest injury will raise further doubts about his long-term future at Old Trafford, particularly with Ten Hag prioritising a new striker in the summer transfer window.
However, there is hope that Brazilian winger Antony will be fit despite being stretchered off during the 4-1 win over Chelsea last week. Antony's ankle injury is not as serious as first thought and he could be available to face City.