The prison houses New Zealand's most dangerous and notorious inmates.
Prison Director David Pattinson said the inmate was taken to hospital by ambulance.
He confirmed an assault was under investigation.
"Staff immediately intervened and secured the alleged perpetrators and provided first aid to the victim," Pattinson said.
"Police are on site and are investigating.
"Corrections will also carry out a full investigation, and will ensure all evidence, including CCTV footage, is provided to police..
Pattinson said violence in prison was not tolerated.
"And anyone who resorts to this behaviour will be held to account, including facing criminal charges," he continued.
"We are constantly working to ensure our prisons provide the safest environment possible for staff and prisoners.
"Auckland Prison is New Zealand's only specialist maximum security facility, and accommodates the country's most dangerous and volatile prisoners.
"Our staff manage some of New Zealand's most dangerous people in a complex and challenging environment."
Pattinson said over 75 per cent of the prison population had convictions for violence in their offending histories, and more than 90 per cent have had a lifetime diagnosis of a mental health or substance abuse disorder.