The O2 - which has previously hosted performances by Kendrick Lamar and George Clinton - also suffered "extensive damage".
They tweeted: "Firefighters are working hard to extinguish the well-developed fire that has taken hold of the Mackintosh building in the Glasgow School of Art".
Labour MP for Glasgow North East and Shadow Scottish Minister, Paul Sweeney, insisted he was "devastated" the building had been plagued by flames again following its 2014 restoration.
Mackintosh's building, which was so unpopular upon construction that its designer wasn't invited to the opening ceremony, became a symbol of the innovative and distinctive Glasgow Style-an global icon of art nouveau architecture.
Eyewitnesses told the BBC that the fire looked "much worse" than the last one. "Glasgow School of Art is an institution that is loved not just by its students, staff and the people of this city, but by many around the world".
A huge fire is raging through the Glasgow School of Art with smoke billowing flames visible for more than 10 miles.
Sylvester Stallone sexual assault claim investigated by prosecutors
County sex crimes task force, which was formed a year ago in the wake of the huge fallout from the Harvey Weinstein scandal. Stallone's lawyer, Marty Singer, said at the time that the actor "categorically disputes the claim".
"This is a blaze, the building is just going up like a tinder-box".
An exhibition by graduating students took place at the nearby McLellan Galleries and the school of art's Reid Building.
"The Glasgow School of Art was a home away from home for 4 years and still such an important part of my life".
The landmark building had been due to reopen next year after restoration.
"The best we can probably hope for is structural facade retention and a complete rebuild of the interior".
The building was designed by artist and architect Charles Rennie Mackintosh and built between 1897 and 1909. "The UK Government stands ready to help, financially or otherwise", he said in a statement.
Others include Doctor Who actor Peter Capaldi, Harry Potter and James Bond movie actor Robbie Coltrane, and members from the Scottish rock bands Travis and Franz Ferdinand.