The historic building, whose spire was shaped as the tails of four dragons intertwined, had been under renovation and clad in scaffolding when the fire broke out.
Parts of the roof had collapsed and the fire spread to several floors of the building, Copenhagen fire department chief Jakob Vedsted Andersen told reporters.
"This is our Notre-Dame! This is a national treasure," emotional local resident, 45-year-old Elisabeth Moltke, told AFP as she watched the blaze.
"A lot of old Danish paintings, originals are in there. I've been in there several times and it's a magnificent building so it makes me feel very emotional."
The fire started at around 7:30am local time (0530 GMT) under the red-brick building's copper roof, emergency services told reporters, as more than a hundred firefighters were dispatched to the scene.
The spire snapped and crashed down onto the street below. Dramatic photographs showed orange flames and huge plumes of black smoke billowing from the rooftop.
Fire trucks surrounded the building, covered in scaffolding and wrapped in tarp and which today houses the Danish Chamber of Commerce.
Ambulances were at the scene but there were no reports of casualties. A spokesman for the company working on renovating the building said the carpenters who worked on the roof had all come out.
Up to 90 members of an army unit were also deployed from a nearby base to cordon off the area and “secure valuables", Denmark's armed forces said.
King Frederik wrote on Instagram that “they woke up to a sad sight” of “an important part of our architectural heritage” being destroyed by the flames.
Prime Minister Mette Frederiksen wrote that “irreplaceable cultural heritage” and “a piece of Danish history is on fire”.
“It hurts to see,” Frederiksen wrote on Instagram.
The stock exchange lies just a stone's throw from the country's parliament and seat of government Christiansborg.
Hard to reach
"It's a copper roof, and it's simply impossible to get under that roof, so the fire has plenty of time to build intensity," fire department chief Andersen told news agency Ritzau, adding that the fire had spread down into the building.
The Boersen building, commissioned by King Christian IV and built between 1619 and 1640, is one of Copenhagen's oldest and best known landmarks.
Housing a vast art collection, it was being renovated to celebrate its 400th anniversary.
"Terrifying images from Boersen this morning. 400 years of Danish cultural heritage going up in flames," Culture Minister Jakob Engel-Schmidt wrote in a post on X, formerly Twitter.
The images recalled the disaster at Notre-Dame Cathedral in Paris, almost five years ago to the day it was gutted by a fire.
Onlookers could not hold back tears as they watched the devastation.
"I'm lost for words ... It's a 400-year-old building that has survived all the other fires that burned Copenhagen down to the ground," said Carsten Lundberg, an employee at the Chamber of Commerce.
"It's a dreadful loss," Lundberg told AFP, adding that what was inside were "things that you cannot put a price on ... Priceless paintings, statues".
A Copenhagen resident reacts as the Old Stock Exchange burns on April 16, 2024. © Ida Marie Odgaard / Ritzau Scanpix via APRushing to save art
Engel-Schmidt said he had been moved to see employees, rescue workers and residents working to "rescue art treasures and iconic paintings from the burning building".
Images from the scene showed several people rescuing works of art, including a painting of the building.
Forces from the Danish military were also called to the scene to try to evacuate artworks.
"We are currently working hard to save our historical art from Boersen," the Chamber of Commerce said in a post to X.
Police said they had blocked off parts of the city centre as part of the fire-fighting efforts.
(FRANCE 24 with AFP, AP and Reuters)
