The Gulfstream G650ER is believed to belong to Graeme Hart, whose wealth is estimated at nearly $13billion.
Flight trackers are unable to track the plane, which was seen sitting on the apron at the airport on Sunday and remained there yesterday.
It is understood the businessman flew a group of pupils from an Auckland school to Dunedin for a University of Otago open day last year.
The university held an open day in Dunedin yesterday.
In December 2018, the Hart family made a $10million donation to the University of Otago towards its dental teaching facility in South Auckland.
A University of Otago spokesman said it could not respond to queries regarding the flight.