It remains unclear if they died due to an accident or foul play.
However, as police have been so far unable to exclude the possibility that a crime was committed, they have classified the case as a suspected murder.
They could not confirm how the woman and child died.
The emergency call was placed at 11am Monday morning to say that two people had been found dead.
An ambulance was sent to the scene at and upon arrival, paramedics confirmed that both were the woman and a young infant were dead and then immediately notified police.
“The case was taken over by the police,” said emergency worker Magnus Loman to the TT news agency.
Whether the woman and child were related is still unclear.
“The identities have not been established,” Åsa Hedin of the Västerås police told TT.
“All we can say is that a woman and a child were found in an apartment, and neither was alive when the police reached the scene.”
Neighbours told the Aftonbladet newspaper that the woman had lived in the area for several years and was “always happy and a fantastic mother”.
According to Norwegian newspaper Verdens Gang (VG), the woman was originally from western Norway, but moved to Sweden in 2008 because she didn’t feel safe in her home country.
Police sources told Aftonbladet that the woman had lived at a secret address for a period as a result of threats made against her.
In 2010, her then boyfriend was convicted in Sweden after assaulting the woman and threatening to kill her.
The woman had six children in all, but only had custody of the youngest, the infant girl found dead in the apartment.
The small town of Arboga was the scene of the 2008 double murder of two toddlers, Max and Saga, who were killed in an attack that left their mother, Emma Jangestig, with life-threatening injuries.
The attack was carried out by Christine Schürrer, the German ex-girlfriend of Jangestig’s then boyfriend, who was sentenced to life in prison for the killings.