Huge flames engulfed the Mackintosh, known locally as the Mack, and spread to adjacent buildings including a night club and a theatre, creating an orange glow over the city skyline.
Efforts to bring the fire under control are expected to be "prolonged", Deputy Chief Officer Iain Bushell said.
A restoration project, which was set to cost between £20 million and £35 million, had been returning the famous art school to its former glory after a devastating fire in 2014, with Brad Pitt and Peter Capaldi among those lending their support.
Firefighters had largely contained the blaze by late Saturday morning after it sweptthrough the art school's Mackintosh Building - described by a local lawmaker as "the most architecturally important building in Glasgow"- and spread to adjoining buildings, including a nightclub.
People gather in the Glasgow city centre as firefighters tackle the fire at the art school. "The fire brigade are now on scene", posted the Glasgow School of Art's Twitter account.
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Nearby buildings that could be at risk from the fire have been evacuated as a precaution, the fire service said.
The school's alumni include recent Turner Prize for art winners Simon Starling (2005), Richard Wright (2009) and Martin Boyce (2011).
GSA director Professor Tom Inns said the fire was a "horrible accident" and a review would seek to learn lessons from it.
"This is a blaze, the building is just going up like a tinder-box".
All of the school's buildings will remain closed for the next week.
Writing on Twitter, Paul Sweeney, a Glasgow MP, said: "It looks like the entire interior space is now fully alight".
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"It is just a shell", she said.
"The Scottish government stands ready to do anything we reasonably can to help ensure that the building has a future".
Secretary of State for Scotland David Mundell, who had visited the building only two weeks ago, said he was "devastated".
Crews were called to the building in the city centre at around 11.20pm on Friday and were met with "extremely hard conditions", he said.
The Mackintosh building was completed in 1909 based on designs by Charles Rennie Mackintosh, Scotland's most-lauded designer.
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