Several neighbours reported hearing loud noises from the property early yesterday, before emergency services were called to the Princes St house at 5.30am.
The infant was rushed to Southland Hospital, and later flown to Starship Children's Hospital in Auckland.
She remained in a critical condition in the hospital's paediatric intensive care unit today, a hospital spokesman said
Inspector Olaf Jensen, of Invercargill, confirmed the parents were in the house at the time of the incident, and police were not seeking anyone else in connection with the incident.
Neighbours said the couple - a Caucasian man believed to be in his 60s and an Asian woman in her 30s - had lived in the large wooden villa for about four years.
The man was known to be a ''hoarder'', but the couple kept to themselves and were very quiet. The baby girl was believed to be the couple's only child.
A neighbour, who declined to be named, said she heard noises coming from near the property around 2.30am, and at 4.30am was woken by what sounded like a ''dog dragging a chain''.
The neighbour said the couple's Saint Bernard dog had been barking for an hour before she left to go to the swimming pool at 5.50am, and she saw four police cars outside the property.
Another neighbour, Vona Tokona (78), said her neighbours were ''a very nice couple'', although she did not see much of them because the drapes were always drawn.
Late yesterday morning, police pitched a tent outside the cordoned-off house and parked a large police truck next to it, while a security guard stood across the street.
Insp Jensen said because an active criminal investigation was under way it was not possible to provide details about the nature of the child's injuries or how they were caused.
He would not comment if any weapons were recovered from the property, as the scene examination was not complete.
That examination, with assistance from Environmental Science and Research, was expected to take place over the next few days.
He told the Otago Daily Times that ''ascertaining the exact timing of the incident will be part of our investigation''.
The parents were not detained by police, and he could not ''comment on their intentions'' when asked whether they had travelled to Auckland.
''Interviewing the parents will be part of the investigation.''
The family were being supported by Victim Support and friends.
