The baby is currently being treated at Christchurch Hospital's intensive care unit.
"Police have spoken to a number of people in relation to this incident who have all been forthcoming in supporting the investigation," Sergeant Anderson said.
"At this stage, police are not seeking anyone else in relation to this incident and are not in a position to make any further comment while the investigation is taking place."
Neighbours were today in shock over the incident.
They say an Indian couple moved there less than two months ago.
Many of the neighbours did not wish to be named but they all spoke about the woman of the household hardly ever venturing outside. Most say they didn't know there was a baby there. Only one woman had known.
"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.
"They've only been there for about two months. I'd seen the girl probably six times but she never spoke or even looked at me. I thought she was pregnant but I never saw a baby there," one elderly neighbour said.
He told of hearing a car honking its horn "five or six times" outside the flat at about 5am this morning.
By the time he decided to get up and investigate, the car "took off at a fair rate".
"I thought, 'What the hell is going on?'"
When the neighbour got up at 7am, he saw a police car outside the property.
"It's just total shock. It's awful," he said. "I've been here since 2001 and never had any trouble. It's always been a very quiet street."
