The 85-year-old completed his takeover at Old Trafford in 2005, acquiring a 90% stake in the club.
A statement on the club's website said: "The thoughts of everyone at Manchester United are with the Glazer family tonight following the news that Malcolm Glazer has passed away. He was 85.
"Malcolm leaves behind his wife Linda, six children and 14 grandchildren. Staff at Manchester United extend deep and sincere condolences to them all at this difficult time."
Glazer also owned NFL franchise the Tampa Bay Buccaneers.