The alarm about a suspected assault in Mälarhöjden came to the police shortly after 2 pm on Thursday.
Police were called to the scene, which was cordoned off.
The police were then silent about what had happened, but a major operation took place at a residential area.
At around 7 pm, the police announce via their website that a woman and a child have died as a result of the injuries.
The woman is said to have died on the spot, while the child was taken to hospital, but the child's life could not be saved.
- What exactly happened on the spot will be investigated further.
I do not want to comment more than that at the moment, says Daniel Wikdahl, press spokesperson at the Stockholm Police.
A man arrested on suspicion of murder
A man was arrested just over an hour later at another location in Greater Stockholm.
The man, who is in his 40s, is suspected of murder.
According to the police, the woman and the child must have a kinship, as well as a relationship with the man, which the police do not want to comment further.
Relatives have been notified.
The place is cordoned off
The crime scene is still cordoned off during the evening and a technical investigation will be carried out.
Among other things, a number of vehicles will be seized and witnesses will be heard.