Live video from local media showed people carrying large paintings away from the building to save them from the flames.
The historic building, whose spire was shaped as the tails of four dragons intertwined, had been under renovation when the fire broke out.
The Dutch Renaissance style building no longer houses the Danish stock exchange, but serves as headquarters for the Danish Chamber of Commerce.
"We are met by a terrible sight. The Bourse is on fire," the Chamber of Commerce wrote on X.
Copenhagen police asked people to avoid driving in the inner part of the city.
(Reporting by Tom Little, Louise Breusch Rasmussen and Stine Jacobsen, editing by Terje Solsvik)
