Police launched a major homicide investigation after the girl was admitted to Christchurch Hospital on Tuesday night by her regular babysitter with assistance from her neighbour.
The girl died yesterday with her parents at her bedside.
Detective Senior Sergeant Scott Anderson said they were now treating the death as a homicide. A postmortem examination will be carried out, the New Zealand Herald reported.
Forensic experts searched the flat yesterday. Neighbours are shocked over the incident. They said a Fijian-Indian couple moved there less than two months ago.
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Meanwhile, the neighbours expressed shock over the incident. Most say they didn't know there was a baby there. Only one woman said she had seen the baby.
"I used to see [the father believed to be in his 30s] carrying a baby in his arms and walk in and out of the front door," one woman said.
The woman of the house, in her mid-20s, is said to have been pregnant with a second child.