The girl was found dead in an apartment in Bro on Saturday night by neighbours and some of her relatives. A 36-year-old man was found seriously injured in the same apartment.
The man has been arrested on suspicion of murder, but is still being treated in hospital and police had not yet been able to question him by Monday morning.
“I can't say [when we will be able to interrogate him]. It will probably be at some point this week,” Anna Frid of the regional police in the area immediately north of Stockholm told Swedish newswire TT late on Sunday.
According to police the man and the girl knew each other.
Bro is a commuter town of around 7,000 people, situated around 40 kilometres north-west of the Swedish capital and the incident has affected the community deeply.
Flowers were left in tribute outside the girl's apartment over the weekend.
“I have not been able to sleep. I haven't closed my eyes for the whole night. I used to watch the girl play on her children's scooter out here in the yard,” one neighbour, named only as Ursula, told Swedish tabloid Aftonbladet.
On Sunday the local church held a special service in memory of the girl.
“We're talking about how to follow this up in order to be there for those members of the parish who are in mourning and are affected by this tragic event,” minister Ann-Carlotte Träisk told TT.
Representatives from the local authority's support group have contacted the girl's relatives as well as her school, said Upplands-Bro council head Maria Johansson.
“Our thoughts go to those close to her. (…) The school is closed for the summer holidays, but we have of course been in touch with necessary contacts,” she added.
Around five children are killed in Sweden every year. The weekend's incident is the second suspected murder in a short period of time.
A nine-year-old girl was stabbed to death two weeks ago in Bålsta, just ten kilometres from Bro, although the two incidents are not thought to be linked. Her father is currently in police custody on suspicion of murder.