The businessman proved a controversial figure at Old Trafford yet oversaw a period of huge success on the pitch since buying the club in 2005.
Under his ownership the club won five Premier League titles and the 2008 Champions League.
Sir Alex Ferguson, the manager who delivered the silverware, had consistently spoken out in support of the Glazers, who were accused by fans of saddling the club with huge debts.
The Glazer family is believed to have sanctioned the sacking of David Moyes towards the end of last season, after he took over from Ferguson in the summer.
It is not thought Mr Glazer's death will have a significant impact on the running of the club, with 90% of shares remaining in the family. His sons, Bryan, Joel and Avram, are on the United board, with the latter two co-chairmen of the club.
A spokesperson for the Old Trafford team said: "The thoughts of everyone at United are with the family."
News of Mr Glazer's death was announced by the Tampa Bay Buccaneers, an American football team which he also owned. In a statement, the NFL franchise paid tribute to him as "a pioneering thinker".
It said: "The Tampa Bay Buccaneers are saddened to announce the passing of Owner/President Malcolm Glazer.
"[His] commitment to building a championship organization has provided the foundation for continued success, on and off the field."