Northland Region Corrections Facility general manager David Pattinson said staff responded immediately to remove the man from his cell and put out the fire.
The other prisoners in the wing were escorted to a secure yard but were returned to their cells shortly afterwards without incident.
Pattinson said the prisoner would face internal misconduct charges and police would be notified.
He said there were no injuries and there was no threat to the wider security of the prison.
"Safety is our top priority and staff respond immediately when smoke is detected. While the fire was already extinguished, as per our normal procedures, Fire and Emergency NZ were called," Mr Pattinson.
Fire and Emergency NZ said it was alerted at 7.45am to a fire in a pile of clothing.
The Kaikohe and Ōkaihau volunteer fire brigades responded, but the Ōkaihau crew was stood down before they reached Ngāwhā, a few kilometres east of Kaikohe.
It's not yet known how the prisoner managed to start the fire.
