The BBC and other media are reporting his name as Glen Malcolm Conning, 50.
Police said four passengers aboard the aircraft were safe.
The pilot was killed immediately after rebels rounded up those on board after the helicopter landed in an isolated area, police said in a statement.
It comes nearly 18 months after the abduction by rebels of another pilot from New Zealand, Phillip Mehrtens, who remains in captivity.
Police said the group responsible for Monday's incident in Alama district in the Central Papua province was the same group that is holding Mehrtens.
The rebel West Papua National Liberation Army (TPNPB) said it had not received a report of the incident cited by police and could not immediately confirm the killing of the pilot on Monday.
A low-level battle for independence from Indonesia has raged in the resource-rich western half of Papua, where attacks by independence fighters have grown deadlier and more frequent as they have procured better weaponry.
A spokesperson for the TPNPB had on Saturday said it had agreed to free Mehrtens, who was kidnapped on 7 February last year after he landed a small commercial plane in the remote, mountainous area of Nduga.
The New Zealand government has repeatedly called for him to be freed immediately and the group has released videos of him multiple times seeking mediation in talks, one with him surrounded by Papuan fighters.
A MFAT spokesperson said it was aware of the reports out of Papua.
"Our Embassy in Jakarta is seeking further information from authorities and we have no further comment at this stage."
