The Scottish fire and rescue service said the call about the fire came in at 11: 19 p.m. Friday local time and that there were no immediate reports of casualties.
"It is hard to find words to convey the utter devastation felt here and around the world for the iconic Mackintosh building", she said.
"My first thoughts tonight are for the safety of people - but my heart also breaks for Glasgow's beloved School of Art".
Sam Patterson, vice president of the Glasgow Institute of Architects, said the spread of the fire throughout the entire building would make any restoration effort extremely hard.
The fire affected all floors of the art school and spread to a nearby campus and a nightclub.
Police have advised the public to avoid the area, and have closed off roads surrounding the art school.
"The Mack has been undergoing restoration since the last devastating fire in 2014".
Nicola Sturgeon has spoken out about the "extremely serious situation".
Asked if any of the restoration work had been destroyed, Mr Heath replied: "I would say, given the extent of the fire, that would be a fair comment".
It has been described as "a working art school as well as a work of art", and has an A-list rating from Historic Scotland.
Stuart Robertson, director of the Charles Rennie Mackintosh Society, said the 2014 fire was contained before damaging the east wing of the building but that this blaze had damaged its entire structure.
The latest fire struck as Glasgow celebrated the 150th anniversary of the architect's birth.
He won a competition to design the building in 1897 and it took around 10 years to complete but is now a landmark in the city, with special government-protected status.
Other former students include actors Robbie Coltrane and Peter Capaldi, and artist Peter Howson.