Officials in Indonesia said Mr Krishnan requested permission to make an emergency landing, but contact with the helicopter was then lost.
Chief Zulfikar, head of the local search and rescue office, said a distress signal was received about 10.30am on Saturday.
Two helicopters scoured the area but that search was soon called off because of bad weather.
Freeport Indonesia spokesman Ramdani Sirait said the wreckage - and three bodies - had been found.
He said the company's emergency response group found the helicopter in a valley in the Mimika Regency of Papua.
A locator beacon had been activated after the Squirrel crashed, but searchers could not initially get to the area because of the rough terrain.
They reached the site hours later and recovered Mr Krishnan's body.
Officials were still working on removing the bodies of his passengers, Adrianus Amba Sangka and Iyan Timisela, who worked for local food supplier Pangan Sari Utama.
Mr Krishnan's family gathered at his Orewa home last night.
He had been working for Queenstown-based company Kershaw Aviation Group for the past 12 months.
The company is contracted to provide helicopter services to Airfast client Mine Serve Indonesia - the exploration arm for Freeport Indonesia and the Grasberg mine.
Its chief executive, Josh Kershaw, said Mr Krishnan was "a very experienced pilot" who had been flying over a route he had travelled many times before.
