The crew of the 18.5 metre (61-foot) vessel San Kawhai was trawling for fish when they brought up the plane in the boat’s nets at about 10am, said Trish Sherson, a spokeswoman for fishing company Sanford.
Police said in a statement that fishermen were transporting the wreckage to a bay near Great Barrier Island, about 90 kilometres (56 miles) northeast of Auckland.
Police said they were heading to the scene with a barge to lift the plane.
They said they were contacting the family of missing Auckland pilot Daroish Kraidy about the discovery.
The 53-year-old pilot took off March 25 in a home-built aerobatic biplane from an airport near Auckland.
Rescuers searched for a week but found no trace of Kraidy or his plane.
New Zealand’s Civil Aviation Authority confirmed Kraidy’s plane was the only one in the country listed as missing.
Kraidy had previously flown in the World Precision Flying Championships.
His ex-wife and daughter told Fairfax Media in May they believed his disappearance was deliberate after he had battled depression for years.
Kraidy’s transponder was switched off soon after takeoff and the plane disappeared from radar screens.
His ex-wife noted some similarities to the disappearance 17 days earlier of Malaysia Airlines Flight 370, with 239 passengers on board.
That plane has not been found.