The batsman had been suffering from lymphoma for a second time, having previously been given the all-clear in 2012.
Auckland-born Crowe is widely regarded to have been one of the best Kiwis to have ever played the game, scoring 5,444 runs from his 77 Test appearances.
He was also named the Player of the Tournament at the 1992 World Cup, during which he scored 456 runs in just nine matches.
Crowe eventually retired four years later because of a long-standing knee injury and he went on to have a successful career in the media.
He is survived by his wife, daughter and two stepchildren.