Surrounding buildings including the O2 Academy concert venue have suffered "extensive damage" as more than 120 firefighters fight the blaze which started in the GSA's Mackintosh building, deputy chief office Iain Bushell said early Saturday.
"This is an extremely challenging and complex incident, but the response and professionalism of our firefighters has been exceptional," Bushell said.
"This will be a prolonged incident and crews will remain on the scene as they work to prevent further fire spread and damage," he added.
There are no reports of casualties or injuries, but residents living nearby have been evacuated from their homes.
The building was in the process of a multi-million dollar restoration after it was ravaged by fire in May 2014 when a projector exploded and set fire to a foam art installation.
The iconic sandstone building is one of Glasgow's most well known and was designed by Charles Rennie Mackintosh at the end of the 19th century. It attracts around 20,000 visitors every year.
Scotland's First Minister Nicola Sturgeon said it was an extremely serious situation.
"Once again, we are indebted to the bravery of our firefighters and other emergency services. My first thoughts tonight are for the safety of people - but my heart also breaks for Glasgow’s beloved (School of Art)," Sturgeon tweeted.
Glasgow City Council leader Susain Aitken asked residents to stay safe, noting there were teams on hand to help those affected.
"Devastating news about the ongoing incident at the Glasgow School of Art. Thoughts with all the emergency services as they work their way through this," she posted on Twitter.
Paul Sweeney, Labour MP for Glasgow North East, tweeted late Friday that the fire was in the most architecturally important building in Glasgow.
"We cannot lose this building," he wrote.