The staff member, reported to be a woman, was working at Hamilton Zoo about 520 kilometres (320 miles) north of the capital Wellington on the country's North Island, on Sunday morning when she was attacked by the animal.
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"Sadly the staff member who was attacked by the tiger has died at the scene," New Zealand police's Senior Sergeant Juliet Burgess of Waikato District Command Centre said in a statement.
"This is a tragic incident. It is too early to determine exactly what's happened. Hamilton Police are working with Hamilton Zoo staff and Worksafe NZ to investigate."
No other details about the attack and the staff member were released by police or the zoo.
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According to the zoo's website, it has an enclosure of Sumatran tigers, which are listed as critically endangered by the International Union for Conservation of Nature.
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