Fire and Emergency New Zealand acting shift manager Jon Ditmer said an automatic alarm alerted firefighters to the incident at the George St facility at 1.22pm, followed shortly after by a 111 call.
Units were sent from Willowbank, Dunedin and St Kilda stations, backed up by Roslyn and Ravensbourne.
The fire was contained, and units had left the scene by mid-afternoon.
A fire investigator was notified.