The aircraft would be inspected by engineers today.
"This aircraft underwent maintenance earlier in the day when engineers replaced an engine component.
"The engine was tested before the aircraft was returned to service."
A Civil Aviation Authority spokeswoman said the authority had been notified about an incident.
She said Air New Zealand was investigating with oversight from the authority.
A passenger, who would not be named, said the flight was due to leave Wellington at 7.20pm.
At 7.15pm passengers were told there would be a delay due to maintenance issues.
They boarded about 8.10pm, he said, but did not take off until about 8.30pm as more checks were being performed.
He said the flight was uneventful until about 10 to 15 minutes before arriving at Tauranga, when the right-hand engine stopped.
"The pilot came on and said we had lost an engine, but he said 'don't worry, that's why we have two engines'."
He said the pilot sounded calm and passengers did not panic.
"There was some general nervousness.
"The most disconcerting thing was hearing the 'clink ... clink ... clink' sound of the propeller."
He said the landing was bumpy but otherwise fine.
"The funny thing was the stewardess apologised for the delay, but not for the rest of it."
