The trooper was taken by helicopter to Auckland City Hospital, where he was later pronounced dead last night.
The soldier's family has been informed and were being supported, the NZ Defence Force said in a statement.
Police were investigating on behalf of the Coroner, while the Defence Force would hold a Court of Inquiry.
The Defence Force said it would not be releasing any more information while next-of-kin were being informed.
The SAS is New Zealand's elite fighting force. In four years from 2013, there were 243 candidates and only 31 succeeded.
Members of the SAS have conducted operations in a diverse range of places, including Malaya, Borneo, Thailand, Vietnam, Bougainville, Kuwait, East Timor, the Solomon Islands and Afghanistan.
Defence Minister Ron Mark is in Fiji for bilateral talks and acting Defence Minister Winston Peters could not immediately be reached for comment on the death.
Many Auckland residents heard helicopters over the city last night that were taking part in a military exercise.
The New Zealand Herald is trying to establish if there is any link between that exercise and the soldier's death.
At least two helicopters - believed to be military-grade Sikorsky choppers - swooped low over Auckland last night, shaking residents' homes before they landed at the Domain and were met by an ambulance.
The choppers were part of a military training exercise but many residents were left bewildered and surprised by the force of their power.
Residents from other central and eastern suburbs also reported the helicopters flying low.
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Comments
Very sad news. New Zealand trains its soldiers hard to fight hard and unfortunately, things like this happen.
In my Army days in Germany during the 80's, large military exercises had built in fatality rates, and deaths were expected and did happen.
Condolencies to his team and family.