Nearby buildings were evacuated as the flames rapidly spread, while more than 60 firefighters worked to contain the blaze.
The Mackintosh Building at the school had been undergoing restoration work since an inferno in May 2014.
More than 60 firefighters and 15 engines were scrambled to tackle the blaze after being called at 11:19pm.
People were evacuated from nearby homes and surrounding streets cordoned off as fire crews battled to control the 'well-developed' blaze.
According to a Rescue Service spokeswoman, there were no casualties in this incident.
