“It started with an argument. That’s all we know,” spokeswoman Kerstin Mälman told news agency TT.
Following a phone call to emergency services, ambulances were sent to an apartment in the Klockaretorpet estate. Ambulance staff found the body of a man at the scene and immediately called the police.
The woman was taken to Vrinnevi Hospital where she later died.
According to Kerstin Mälman, the exact identities of the victims are not yet known. Police have not released details of any weapons that may have been used in the attack.
“We have to take a look at this and find out what happened after the forensic team has completed its initial investigation,” she said.
There have not been any arrests in connection with the deaths.