Emergency services discovered the grisly scene after being called to a Timaru home around 10pm on Thursday night.

The dead are twin girls aged two and their sister, aged six.

A 40-year-old woman also suffered injuries and was taken to Timaru Hospital.

Detective Inspector Scott Anderson said the residents of the house were a family who "arrived from South Africa in the last week".

"The investigation into this tragedy is still in its very early stages but we can confirm that no one else is being sort in relation to the deaths of the three children," he said.

Mr Anderson said the hospitalised woman was in a stable condition.

Neighbours have told local media they heard a man "crying and wailing" outside the property prior to the arrival of the police, saying "is this really happening?"

"We asked him if he was okay. He did not respond to us and was screaming and crying hysterically," neighbour Karen Cowper told Stuff.

A woman is due to appear in the Timaru District Court on Saturday morning, the NZ Herald reported.

The deaths are the second tragedy in as many months to befall the South Island port city.

Last month, five teenage boys were killed in a one-car crash in which only the 19-year-old driver survived.

That crash was the South Island's worst car accident in a number of years.

Timaru Mayor Nigel Bowen told the Otago Daily Times his community of around 30,000 has endured "layers of tragedy".

"I think the community will be thinking, why is it happening to a place like ours?" he said.

"There's a lot of pressures on society at the moment, you have to question the support around mental health.

"Are we doing things right in this country? I question that we're probably not."

In a separate incident, police have arrested and charged a 23-year-old man for the murder of a 16-year-old girl, whose body was discovered last Saturday.

The dead teenager's family described her as "a very beautiful butterfly" in the NZ Herald.

Detective Mike Hayward said "the victim was a young girl who was extremely loved by her family and friends and they are absolutely devastated by what has happened to her".

Australian Associated Press