Four rescue helicopters have been dispatched to the scene at Fox Glacier on the remote west coast of the South Island, a New Zealand Rescue Co-Ordination Centre spokesperson said.
A paramedic will be winched down to the crash site to assess the situation and a cliff rescue team is also being sent to the area.
Weather conditions around the glacier were described as "terrible" with heavy rain and poor visibility.
"It wouldn't be a good day to be flying helicopters," Grey District Mayor Tony Kokshoorn told the New Zealand Herald.
"Everything is against a rescue (mission). It will be cold up there. And the problem is amplified by the cloud cover.
"It is terrible," he said. "We just have to wait and see if there are any survivors."
The downed helicopter was reported to belong to Alpine Adventures, a company that advertises itself as an "experienced helicopter flight-seeing company providing visitors with a diverse range of South Island scenic helicopter flights and private charters in some of most spectacular alpine and coastal regions of New Zealand".
Fox Glacier is 13 kilometres (eight miles) long and is listed as one of the most accessible glaciers in the world.
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