Corrections will carry out a full investigation, and ensure all evidence, including CCTV footage, is provided to police, Beales said.
Corrections Association president Alan Whitley told media outlet Stuff he understood the prisoner had been stabbed.
Police confirmed the incident was also reported to them this afternoon
"One person sustained serious injuries and despite being provided medical assistance, they have died at the scene," a police spokesman said.
Police were making inquiries to establish the circumstances of the death.
"At this early stage police are not in a position to comment further," the spokesman said.
St John were called to the prison at 2.40pm, a service spokeswoman said.
"We deployed one manager and two ambulances," she said.
Paremoremo Prison is New Zealand's specialist maximum security prison and houses the 28-year-old man accused of the Christchurch terror attacks.