The Korean-born New Zealander is charged with murder.
The woman in her 40s was arrested in the southeastern city of Ulsan earlier in the day, after global police agency Interpol issued a red notice, the Korean National Police Agency said.
The woman is suspected of fleeing to South Korea in 2018 after killing her then 7-year-old and 10-year-old children in Auckland, authorities said.
A South Korean court will review whether to extradite the suspect to New Zealand, they added.
New Zealand police launched a homicide inquiry in Auckland after the remains of the children were found by a family going through the contents of a storage locker they had purchased unseen.
The family who found the bodies were not connected to the deaths.
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