The family, consisting of a husband, his heavily pregnant wife and their six children, had fled to the cellar after being evicted from their previous address.
The woman was moved from Gävle to Karolinska Hospital on Monday morning for further treatment.
“It is not certain why they were living there but I suspect they may not have known about the safety nets available,” said police spokesman Max Forsstöm.
According to one of the children, the family had been living in the cellar for three days after they were asked to leave the address in Gävle where they had been staying with a relative.
The family has lived in Sweden for ten years, and several of the children, aged between 5 and 14, were born in the country. The family members have residency permits and has never previously been in contact with the police.
The cellar where the family sought refuge is located in Tolvfors, a small area on the outskirts of the eastern town of Gävle consisting of stables, paddocks, streams, a community centre and an old manor.
The cellar is an old storage building constructed for the conservation of vegetables and other foodstuffs.
On Sunday evening the family tried to light a fire in the cellar to generate some warmth.
The night was relatively mild and damp but previous nights had seen temperatures drop below zero.
“They had put up some form of covering in the doorway, presumably to keep out the cold,” said Max Forsström.
But it also led to them inhaling dangerous smoke fumes.
Tolvfors is located near Gävle Hospital and the father of the family went there to get help. Emergency services and police were quickly called to the scene.
Though their mother has been taken to Uppsala, the six children, three boys and three girls, are still being treated at Gävle Hospital.
Since their father is also undergoing treatment the children will remain at the hospital until social services staff in Gävle have managed to find housing for the family.
“There is absolutely no suspicion of crime. Social services have been alerted.
“But first of all they will all get treatment. Then they will get help,” said Forsström, adding that the family’s situation is deeply tragic.