© AFPFire engulfed the historic spire which then collapsed
The 17th Century Børsen is one of the city's oldest buildings and onlookers gasped as its iconic spire collapsed in the flames.
Everyone inside the building was able to leave and people rushed to rescue some of its historic paintings.
Culture minister Jakob Engel-Schmidt said 400 years of Danish cultural heritage had gone up in flames.
The building, dating back to 1625, is a stone's throw from Denmark's parliament, the Folketing, housed in the old royal palace of Christiansborg castle. Danish media said the nearby square was being evacuated.
Danish chamber of commerce director Brian Mikkelsen joined ambulance workers in rescuing the building's art treasures
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The old stock exchange was being renovated and had been shrouded in scaffolding and protective plastic covering. It currently houses the Danish chamber of commerce, which described the scenes on Tuesday morning as a terrible sight.
Local craftsman Henrik Grage told Danish TV that it was a tragic day. "This is our Notre-Dame," he said, comparing it with the fire that engulfed the roof and spire of the cathedral in the centre of Paris almost exactly five years ago.
The Paris fire broke out under the eaves of Notre-Dame on 15 April 2019 when it was also shrouded in scaffolding as part of extensive renovations. Investigators have blamed either a short circuit in the electrics or a worker's cigarette butt that was not properly put out.
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The cause of the fire in Copenhagen is also for the moment unknown but emergency services said the scaffolding made their operation more difficult. Much of the building is thought to have been badly damaged by the fire, which officials say was most intense around its tower.
Emergency services chief Jakob Vedsted Andersen said firefighters faced an almost impossible task accessing the area under the old copper roof.
"I'm completely speechless - this is an unparalleled tragedy," one onlooker told Danish media.
Members of the public joined emergency services, as well as chamber of commerce director Brian Mikkelsen, in rushing into the building to save the Børsen building's substantial art collection.
Prime Minister Mette Frederiksen spoke of "terrible images" and of a piece of Danish history going up in flames.
Local museum inspector Benjamin Asmussen told Denmark's TV2 that the fire was difficult to watch, as the old stock exchange was filled with paintings of Danes who had played important roles since the 17th Century.
King Frederik X said the fire was a "sad sight" for such an important part of Denmark's cultural heritage: its characteristic dragon spire had helped define Copenhagen. He succeeded Queen Margrethe II in January and events for her 84th birthday planned on Tuesday were being toned down because of the fire.
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The Dutch Renaissance-style building on the city's Slotsholmen, or palace island, was commissioned by Denmark's King Christian IV with the aim of turning Copenhagen into a major trading centre.
The famous spire featured four dragons whose tails were twisted into a spear and three crowns, symbolising close ties with neighbours Norway and Sweden.
While only "historic", it is still a stock exchange.