Firefighters used a high-volume water pump from the River Clyde to tackle the blaze at the Glasgow School of Art.
The operation has led to a number of road closures in the city centre.
The roads affected are Broomielaw, Brown Street, Argyle Street, Douglas Street and Dalhousie Street. Closures also remain in place around the Sauchiehall Street area.
Police Scotland have asked motorists to avoid these areas.