That annex, which lies in the block behind the Old Stock Exchange, was evacuated as a precaution, as were different ministries in the street behind the burning building.
Beside housing the Chamber of Commerce, the Old Stock Exchange is used for gala dinners, conferences, parties and other events.
Police said on the social media site X that a main road in Copenhagen was closed and people should expect the area to be cordoned off for some time. Several bus lines were rerouted and Danish media reported huge traffic jams in the surrounding area.