Airways New Zealand, which manages air traffic control, said all flights, including international and domestic services, were affected.
A spokeswoman for the government agency said technicians were working to find the cause of the problem but it was impossible to say when it would be fixed.
"There has been a radar failure that has occurred at 2.48pm (local time) this afternoon, we are working on the issue at the moment," she told AFP.
Airways NZ's website says it manages 30 million square kilometres of airspace, handling about one million aircraft movements annually.
Auckland airport, the country's largest, warned travellers to expect delays.
