“She died at around lunchtime as a result of her injuries,” said Christer Claesson at Karolinska University Hospital.
The girl therefore brings the death toll to seven after the deaths of her 42-year-old mother and five of her siblings, aged one to 16, on Saturday.
An eighth member of the Somali family has been treated for minor injuries sustained in the fire.
The technical investigation to determine the cause of the fire continued on Tuesday. Technicians from the National Laboratory of Forensic Science (SKL) have spent the day examining the burned out apartment in Rinkeby.
“We hope that their expertise will enable us to establish the cause of the fire or at least to rule out possible causes,” Peter Saarman, a spokesperson for west Stockholm police told news agency TT.
According to the police an analysis of the fire could be completed within a couples of days after the completion of the investigation.
“Then we will hopefully know more about what caused the fire,” Saarman said.
Saarman was asked by TT if the fire was caused by a technical fault.
“Details along those lines have emerged, but that it nothing that I can either confirm nor deny at the moment, as we do not yet know.”
According to the police the girl died as 1.04pm. She had been in the care of the hospital since Saturday night and had been lying unconscious in intensive care.
“Her status has been critical the whole time and she has been swinging between life and death,” Saarman said.
The tragedy is the deadliest in the Scandinavian country since 1998, when a fire in the city of Gothenburg killed 63 people.