"The person is on the asylum centre's roof. Police and emergency workers are on location and the residents of the centre are being evacuated," the police said in a press release.
It was not yet clear whether the person was an asylum seeker.
A flight ban was issued above the asylum centre, which applied to all aircraft and drones.
The incident was reportedly taking place at Asylcentre Nyborg, an asylum centre with a capacity of 500 occupants.
Denmark registered 21,000 asylum applications in 2015, making it one of the main EU destinations for refugees per capita, after Finland, Austria, Germany, and Sweden.
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