Forensic investigators outside the home in Auckland's suburbs were the bodies were found last month
In a case that shocked the country, the remains were discovered by strangers who bought the suitcases from a storage unit in Auckland.
The bodies had been stored for several years. Police say the victims had been aged between five and 10.
New Zealand has applied for the woman's extradition from South Korea.
Police said they had worked closely with South Korean authorities over the past three weeks in the search for the woman, after saying last month that they believed she was in South Korea.
They zeroed in on her after managing to identify the young children, whose names have not been disclosed.
"To have someone in custody overseas within such a short period of time has all been down to the assistance of the Korean authorities and the coordination by our NZ Police Interpol staff," said Detective Inspector Tofilau Fa'amanuia Vaaelua.
He said the woman was arrested by South Korean police on Thursday morning, and New Zealand authorities would apply for her to be denied bail prior to her extradition.
He added the public had offered "overwhelming support" for the police operation.
Local media has reported the suspect is believed to be related to the children. They said the family had lived in Auckland for a few years and the children's father had died prior to their deaths.
Police said the family who found the bodies had visited the storage unit and purchased a trailer-load of goods, including the suitcases, in early August.
That family had no connection to the deaths and had suffered great distress in the period following the discovery, officers said.
-- Courtesy of BBC News