The widely criticised law makes it easier to punish protesters and reduces the city's autonomy.
Travel advice has also been updated to alert New Zealanders to risks presented by the law.
China's embassy in New Zealand said the suspension was a "gross interference in China's internal affairs".
"The New Zealand government's decision is a serious violation of international law and basic norms governing international relations," a statement said.
Canada, Australia and the United Kingdom earlier suspended their extradition treaties with Hong Kong.
Military and dual-use goods and technology exports from New Zealand to Hong Kong will now be treated in the same way as New Zealand treats such exports to China.
New Zealand Foreign Affairs Minister Winston Peters said China had "eroded rule-of-law principles, undermined the 'one country, two systems' framework that underpins Hong Kong's unique status, and gone against commitments China made to the international community".
Hong Kong's government says the law is required to bring order to a city that saw mass pro-democracy protests last year that often turned violent.