"It appears to be a family tragedy," Tobias Lövström of the police told the Aftonbladet newspaper.
According to the Dagens Nyheter (DN) newspaper, the victims include a 55-year-old man and an 11-year-old boy. Both were found in a flat on Styrmansgatan.
Police remain rather tightlipped about the fatalities, which were reported around 11am on Monday by an acquaintance of the 55-year-old who was unable to contact the man.
Sources told Aftonbladet the victims had been dead more than a day, and police have launched an investigation into suspected murder.
The 55-year-old is registered with the police as a licensed gun owner, but police refused to reveal any details about how the man and the boy were killed.
Follow The Local on Twitter