The prisoner was evacuated to the yard while fire crews from the Harewood, Wigram and Rolleston stations put out the blaze about 4.50am.
The prisoner was not hurt but the cell was "extensively damaged".
Eight prison staff were sent to the medical centre to be treated for possible smoke inhalation.
Corrections will carry out a full investigation and Worksafe NZ and police have been notified.
Fire and Emergency New Zealand spokesman Andrew Norris said firefighters were at the prison for about 45min.
The cell was empty by the time the crews arrived.
Corrections said a full debrief will take place and support will be provided to staff.
The fire comes after an incident at the prison on October 29 in which five men had a drunken party in a make-shift swimming pool made out a of water-filled rubbish skip.
The group included a high-risk sex offender who once escaped from the jail in a food truck. They also attacked a prison guard.
