Crews from Hampshire and Isle of Wight Fire and Rescue Service attended Princes Court on Northam Road following a call received at 8.21am.
However, by the time firefighters arrived, the fire had already been extinguished. The incident was confirmed as closed at 8.29am.
Two fire engines were sent to the scene. No injuries have been reported and the cause of the fire is not yet known.
HIWFRS has been contacted for further information and updates will be published when available.