A welcome ceremony was set to be held later in the day at the official residence of Governor-General Patsy Reddy, according to Moon's presidential office Cheong Wa Dae.
Moon and his wife, Kim Jung-sook, will hold a brief meeting with the governor-general and her husband, David Gascoigne, before attending an official lunch to be hosted by them.
The South Korean president will later hold a meeting with South Korean residents in New Zealand.
He will hold a summit with Prime Minister Jacinda Ardern on Tuesday.
Moon will head home later in the day, wrapping up an eight-day trip that has also taken him to the Czech Republic. (Yonhap)