Allen, who coached the All Blacks from 1966 until 1968 and was known as The Needle, had been battling ill health for some time and was in full-time care.
A fly-half, he played 21 matches for the All Blacks between 1946-49 and captained the side in all of them - but it was as a coach he made a major impression.
During his spell in charge of New Zealand, one of the team's greatest eras, all 14 Tests matches played were won.
He was knighted in 2010 and had been inducted into the New Zealand and International Rugby Halls of Fame.
A family statement read: "It is with great sadness that his family advises of the death of Sir Frederick Richard Allen, on April 28.
"Sir Fred passed away peacefully in the early hours of the morning at Maygrove Village Hospital, Orewa, where he has resided in recent months.
"His record as a player and coach of the Auckland rugby team and as a player, captain, selector and coach of the All Blacks has been well documented.
"He was forthright and inspirational and his services to Auckland Rugby and many other sporting and non-sporting organisations reflected his ever present passion and generosity of spirit.
"Earlier this week, Sir Fred had participated in the opening of a bridge at Auckland Memorial Park and at an Anzac Day service."
Allen's wife Norma died in 2009. He is survived by his daughter Marianne and granddaughters Inés and Katia."
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