Investigators are at the scene as firefighters continued to dampen down the fire at the Mackintosh building, which broke out late on Friday and spread to the neighbouring O2 ABC music venue.
The inferno, which rapidly took hold, comes four years after the property, hailed as an architectural masterpiece, was badly damaged in another fire.
The building had been undergoing a multimillion-pound restoration programme, which had been due to be completed next year.
Fire crews say the damage caused in the 2014 blaze was considerably less than that suffered in the latest disaster.
Visiting the site, Scotland’s first minister told reporters: “It is heartbreaking.”
She said her government was “ready to do anything we reasonably can” in the wake of the blaze.
Ms Sturgeon said it was too early to draw conclusions on what may have caused the fire as she hailed the efforts of emergency workers at the scene.
Scottish Fire and Rescue Service deputy assistant chief officer Peter Heath said the building had been “extensively damaged by fire” that had “spread very rapidly”.
Crews called to the building in the city centre at about 11.20pm on Friday and were met with “extremely difficult conditions”, he said.
At its height, more than 120 firefighters were battling the flames.
“This fire has consumed this building,” said Mr Heath.
The blaze was a “devastating loss for Glasgow”, with firefighters dealing with a “sense of loss” along with the city’s people, he said.
Architectural historian Neil Baxter told Sky News the building was of global importance, having influenced architecture around the world since its creation in the 19th century by Charles Rennie Mackintosh.
“It’s just tragic,” he said.
Former students at the art school spoke of their shock and sadness.
Graduate Margaret Archbold, 48, said she had come to the cordon surounding the building to “say goodbye”.
She said: “It just keeps getting kicked in the teeth. It shouldn’t have happened again.
“It was graduation day yesterday for this year’s students. I just feel really sorry for the fire brigade because they worked so hard to save it the last time.”
Sam Patterson, 30, vice president of the Glasgow Institute of Architects, who studied at the art school, said there was a sense of “disbelief”.
Mr Patterson said: “It’s a shocker, especially in Mackintosh’s 150th anniversary and so close to being completed.”
Stuart Robertson, director of the Charles Rennie Mackintosh Society, said the fire was “terrible” and a “massive body blow” and would be “sending shockwaves around the world”.
He said: “This is a world class building. With all the restoration work going on it’s just horrendous, I can’t really believe it.
“I’ve only seen glimpses, and what the firemen are saying, reading between the lines it looks bad. The last time they stopped it going into the east wing this time it looks as though it’s gone from the east wing all the way through.
“To see some of the work and the beautiful craftsmanship that’s gone on and I’d seen a glimpse of the new library taking shape and the studio work and all the painstaking work that’s gone into the restoration is just… people must feel sick.”
Alan Dunlop, professor of architecture at the art school, said he was “devastated”.
He said: “It’s horrible. The building does look as though from the inside it’s been totally gutted. All that seems to remain is the stone walls on the outside.
“The deeply sad thing is that yesterday was graduation day. So the students will have felt elated and very happy, and then to wake up the next morning they will be very sad indeed.”
Hollywod star Brad Pitt and Dr Who actor Peter Capaldi were among those lending their support to the restoration project, which was set to cost up to £35m.