The prisoner who died at Otago Correctional Facility on Tuesday was David Joseph Jackson.
The 29-year-old was found in an unresponsive state and given medical attention, but was pronounced dead at the scene.
His death has been referred to the coroner and is subject to an investigation by the prison inspectorate and police.
St John communications adviser Ian Henderson said three ambulances were sent to the prison at about 4am.
The Milton Fire Brigade also attended and helped with medical treatment.
