Eyewitnesses said the fire appeared to have started when a projector exploded in the basement of the Charles Rennie Mackintosh building just before 12:30.
Twitter users in the Scottish city are posting images showing plumes of black smoke billowing from the building, which was built between 1899 and 1909. Flames can be seen engulfing windows on the top floor of the school.
"The smoke from the fire at Glasgow School of Art is visible from seven miles away," wrote @idea15webdesign. "This is awful". Sunday Times architecture critic Hugh Pearman tweeted: "This can't happen. We can't lose Mackintosh's Glasgow School of Art. It's unthinkable."
Charles Rennie Mackintosh was a 28-year-old junior draughtsman at a Glasgow architecture firm when he drew up the designs for the building that many consider his masterpiece.
The first half of the Glasgow School of Art building was completed in 1899. But the dramatic art nouveau design of the building in the Garnethill area of the city centre took another 12 years to be completed, finally opening in 1909. It heralded the birth of a new style in 20th Century European architecture.
It is now considered one of Scotland's most admired and influential buildings and Mackintosh, under-appreciated in his own time, is lauded as one of the country's finest designers.
Update 5.30pm, Friday 23 May:
In a statement published on the Glasgow School of Art press site, Muriel Gray, chair of the board of trustees of the Glasgow School of Art, said: "today is a really black one for the GSA, but I cannot thank the fire brigade enough for the speed with which they came and their commitment to contain and extinguish the fire. Fortunately there have been no fatalities or injuries."
"I am so proud of the staff and students and how everyone has pulled together. We are thankful to all the Glaswegians who turned up to comfort students and to friends from across the world for their messages of support."
The fire is thought to have been started by an exploding projector that set light to expandable foam used in an art installation.