Glen Malcolm Conning, 50, of Motueka was killed by a pro-independence group known as Free Papua Organisation (OPM) when rebels rounded up those on board the helicopter, including four passengers, after they landed in an isolated area in the Central Papua province.
The passengers are reported to be safe.
In a statement released on Tuesday by Natasha Conning on behalf of his family, they say he is truly loved by his family and friends, who he cherished spending time with when he wasn't flying or being in the outdoors.
"Our hearts are broken from this devastating loss."
They say they appreciate the love and support they have received, but ask for privacy at this time.
Conning was shuttling passengers for a private company.
A spokesperson for the police special operation in Papua, Bayu Suseno, claimed his body was taken to the helicopter and then burned along with the aircraft in Alama District, which can only by accessed by helicopter.
OPM spokesman Sambom told the BBC that despite being unable to verify the claims, "if it was true, then the pilot is a spy because we have declared that the area is a war zone".
In February 2023, separatist fighters in Indonesia's Papua region took another New Zealand pilot hostage.
Phillip Mehrtens, 37, was captured shortly after landing his plane in the remote mountainous area of Nduga to drop off passengers.
Since then, Mehrtens has been held captive by West Papua National Liberation Army fighters (TPNPB) - the armed wing of the OPM - who also attacked a number of Indonesian troops sent to rescue him, killing at least one.
These hostile acts come in the context of a long-running, often brutally violent conflict between the Indonesian government and West Papua's indigenous people.
Papuan rebels have been seeking independence from Indonesia for decades, and have previously issued threats and attacked aircraft which they believe are carrying personnel and supplies for Jakarta, the country's capital.
The region is divided into six provinces and is separate from independent Papua New Guinea.
Previously a Dutch colony, West Papua declared independence in 1961. However, Indonesia took over two years later and was formally given control in a United Nations-supervised vote in 1969.
The UN vote is widely considered illegitimate as only about 1000 Papuans took part in it.
A pro-independence movement began shortly afterwards, which continues to this day.
