Sir Michael was representative of the Sovereign from 1996 until 2001.
Prime Minister Christopher Luxon today paid tribute to him on social media in announcing the death.
"His distinguished life of service to New Zealand was one of dedication and reliability," Luxon wrote.
"Sir Michael epitomised what it is to be a great New Zealander. Our thoughts are with his family at this time."
Sir Michael was born in 1931 in Wellington.
A former High Court and Court of Appeal judge, he was chosen to oversee the first two elections held under the MMP system due to his legal experience.
"Sir Michael guided New Zealand into the MMP era," Luxon said in the statement.
"Sir Michael was a figure of stability during a time of significant constitutional change."
He was knighted in 1995 and the following year became the first Knight Grand Companion of the New Zealand Order of Merit.
Sir Michael believed Governors-General had a duty to speak out about the community's concerns - which he did, commenting on inequality, family violence and child abuse.
When his vice-regal term ended in April 2001, he retired from public life.
In accordance with Sir Michael's wishes, a state funeral will not be held.
Further details will follow from the family in due course.
Sir Michael married Mary Zohrab in 1957, and they had four children (two daughters, two sons) and several grandchildren.
