"Probably the man killed the woman and then took his own life," said Richard Florén at Stockholm police to the TT news agency.
"No one else has been inside the apartment and it has been locked. The appearance of the apartment and the location of the knife which has been used have also been considered. There is no evidence to suggest anything else," Florén said.
The couple were found by an acquaintance who alerted the police shortly before 10pm on Thursday.
Police believe that the man and woman had an ongoing relationship, but there are no children affected.
The apartment has been examined by police forensic experts and the bodies will be sent for forensic examination.
According to a report by the Swedish Association of Women’s Shelters and Young Women’s Empowerment Centres (SKR), every third woman worldwide is a victim of physical, sexual or another type of violence during her lifetime.
The Cause of Death project shows that while the vast majority of Swedish women live in relative equality equal, free from violence, some 17 women are killed each year at the hands of either their husband, boyfriend, ex-husband or ex-boyfriend.