McLaren Automotive was inspired by the legacy of late New Zealand racing driver Bruce McLaren and his eponymous racing team.
Last January, NZME reported McLaren delivered one of the cars to a New Zealand citizen. The buyer, who requested anonymity, reportedly paid $1.8 million for the car.
Other media said the car was delivered to a new owner in Hawkes Bay.
The car was not currently listed on the New Zealand Transport Agency (NZTA) safety recalls database.
An NZTA spokesman was investigating.
A McLaren Auckland staff member said he wasn't aware of the recall and couldn't comment at this stage.
The P1 had a top speed of 395km/h and could reach 100km/h in 2.8 seconds. It had a 3.8-litre twin-turbo V8 petrol engine coupled to an electric motor.
Top Gear said every P1 took around 800 hours to produce, with 105 different people involved in the making of each one.
North and South America received about 34 per cent of the cars and Europe about a quarter, Top Gear added.
McLaren launched its first road car, the F1, in 1993.
New Zealander Roger Donaldson, who directed The World's Fastest Indian, is directing the documentary McLaren, about the race car driver's life.