The glitch began about 9.30am and was resolved by about 1pm, an airport spokesman said.
The arrival time of several flights from locations including Melbourne, Brisbane, the Gold Coast, Dubai and Suva have been delayed by up to an hour.
The Herald is seeking how many people have been affected by the delays caused.
The Auckland Airport website still showed at 1.20pm several flights had either been delayed or rescheduled. They include flights coming from Papeete, French Polynesia, Dubai via Melbourne or Brisbane, Shanghai, Suva, Melbourne, Gold Coast, Brisbane and Sydney.
There were also major delays at Sydney, Melbourne and Brisbane airports due to the computer software problem.
News.com.au reported that a global computer software system, which allowed airlines to check passports, was down.
A Melbourne airport spokeswoman told the publication: "This system is used globally, so the issue affects many other airports as well as Melbourne".
An Auckland Airport spokesman said it had an impact on passengers wanting to leave Auckland today.
Mark Croudace, manager passenger and terminal operations at Auckland airport said up to nine arrivals were expected to be delayed by as many as fifteen minutes this afternoon.
Flights showing more significant delays were unrelated to the immigration system glitch. Passengers on four or five flights departing Auckland had experienced delays earlier today but no one was believed to have missed their flight, Croudace said.
Immigration New Zealand national manager for borders Senta Jehle confirmed in a statement there was a technical issue with its Advance Passenger Processing (APP) system.
It had not been working since 9.30am.
"INZ is working with its providers to get the system up and running as soon as possible. In the meantime INZ is using manual back- up systems, which could cause some delays to passengers checking in for flights to New Zealand from overseas and when they arrive in New Zealand."
When passengers check in overseas, APP validates their entitlement to travel to or through New Zealand. Passenger information entered into airlines' systems is screened against Immigration New Zealand's database at time of check in. Check- in agents are now relying on manual checks with INZ staff to verify information, Jehle said.
Australian airports also use the APP system.
A spokesman for Wellington Airport confirmed the outage affected them too. The system system allowed airlines to report on the border clearance process.
"Airlines will be manually checking passports until the system is restored.
"The next international flight to leave Wellington is at 1515hrs, so airlines and airport staff are preparing in advance.
"International passengers should expect some delays due to the manual check-in but should check with their airline for latest information."