A spokesperson for the airport said it was closed to air traffic due "a potential security event".
"We take the safety and security of our staff, Airways' staff, and the public seriously.
"As such, as a precautionary measure, the tower and runway were closed while police investigated."
The statement said that "for staff welfare reasons" the tower and runway will remain closed at this stage and a further update about when the airport will reopen is expected tomorrow.
Earlier this week the University of Otago abandoned several graduation ceremonies after threats, including a warning of a shooting.
The Otago Daily Times confirmed the warning was sent by email and also included a threat of a bombing.
Police declined to comment on the nature of the threat.
"While we understand people want to know the specific nature of the threat, at this stage of our inquiries we cannot provide this detail as it could compromise the outcome of the investigation.
The cancellations affected hundreds of students, many of whom had earlier graduation ceremonies postponed due to the Covid-19.