"Prisoners and staff affected by the man's death are being provided with support.
"All deaths in custody are referred to the Coroner for investigation and determination of cause of death. For all deaths in custody, there is also an investigation by the independent Corrections Inspectorate.
"As the death remains subject to investigation, and the Coroner is yet to determine the cause, we are limited in the amount of detail that we are able to provide."
A spokeswoman for the Wellington Free Ambulance Service earlier said two ambulances and a response vehicle were called to the prison just before 10am on Sunday.
Rimutaka Prison in Upper Hutt is one of New Zealand's largest prisons, with 805 prisoners as at last September. It opened the country's first container-cell unit in 2010.