The victim was found in a property on Norra Grängesbergsgatan in Malmö. He was rushed to hospital but was pronounced dead upon arrival.
The police have detained a 58-year-old man and have questioned three witnesses, but said they did not yet know what had prompted the shooting.
"It's too early to speculate about a motive for the shooting," police spokeswoman Linda Pleym told the TT news agency.
The police have cordoned off the scene of the crime, which has attracted a large crowd of curious onlookers. The first patrol was sent out after a call came in at 12.37pm. The officers found the man shot in the building, with several people present at the scene.
The suspect, who was detained nearby, was known to the police from previous incidents, but a spokesperson declined to give further information.
Witnesses told TT they heard five shots ring out in the blighted area, where residents testified that the neighbourhood had become increasingly rough. The victim was found in the same property that was subjected to a bombing last year.
"It's not good that they are shooting and setting off bombs here," one witness, who said he wanted to remain anonymous for fear of reprisals, told TT.
Another man present in the area on Friday told TT that he had run a business in the industrial area just outside Malmö city centre, but had closed shop.
"This area really is dangerous and criminal. I was scared, we were burgled twice," said the man, who also chose not to give his name. "They (the police) should check who rents properties here, because there are a lot of criminals and a lot of illegal clubs."