The tragic incident took place at the Geijersholm detention centre in the town of Hagfors.
"I don't know if he had any relatives or family," Stefan Wickberg, a spokesman for the local police, told TT.
Police were called to the scene around 8.30 PM on Tuesday after a fight broke out. The man who was later shot had reportedly hit someone in the head and was drunk. An ambulance was also on the way to the scene.
When police arrived, the man was wielding a knife and banging on a door, said police spokesman Tommy Lindh. He reportedly threatened the police officers, one of whom pulled his gun and fired one shot.
"The first shot had no effect. The man continued to attack. That's when the policeman fired a second shot and the man fell down," said Lindh.
According to the police, the man died at 9.27 PM.
"This is first and foremost a police case and it is obvious that something went terribly wrong. We are now sending staff to the area to answer questions and to act as support," said Fredrik Bengtsson, a spokesman for Swedish Migration Board (Migrationsverket),
According to the Migration Board, the refugee centre houses 38 people in 18 apartments. The fatal shooting will be investigated by the Swedish National Police-related Crimes Unit (Riksenheten för polismål).
Two police officers have been taken off duty and residents at the refugee centre said they felt both angry and sad after the incident.
The incident marks the fourth fatal police shooting in Sweden this year.