One witness told Danish media that five or six shots were fired.
Police said a man had been arrested and a sawn-off shotgun recovered at the scene.
A press release from the police later revealed that two men had been shot near the bailiff’s court on Hestemøllerstræde near Town Hall Square.
Streets surrounding the court have been cordoned off. The motive for the shooting was unclear, police said.
A preliminary hearing was taking place in the court when the firing broke out.
The police announced that the suspected gunman was in custody and that a sawn-off shotgun had been found.
Jyllands-Posten reports that the police are asking people to stay away from the area and are patrolling in large numbers with machine guns.
A family row may have sparked the attack which took place at about 10:00, Danish media reported.
The head of Copenhagen city court, Soeren Axelsen, said he thought that was the most likely reason for the shooting as the court dealt with family-related cases as well as debts and bankruptcy.
The first victim died at the scene and the second was taken to hospital with life-threatening injuries, Danish TV said.
A witness told reporters that the gunman fled the court and was later arrested in a street beside Copenhagen town hall.
Soeren Axelsen said counselors had been brought to the court to help staff deal with the attack.
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