"And then because the runway was closed from 1.30 to 4.30am, they told them they weren't going to be able to depart until 4.30am."
The airport spokeswoman said there was scheduled maintenance every Monday morning.
An Air New Zealand spokeswoman confirmed the pilot did not show up.
"Unfortunately one of the crew members on [Monday's] NZ282 service to Singapore did not report for duty on time due to mis-reading his roster.
"By the time the mistake was established we were unable to get this crew member or a standby crew member to the airport prior to the runway closure and had to wait until it reopened to depart.
"The crew member understandably feels incredibly embarrassed about what was clearly a genuine mistake."
Passengers were due to touch down in Singapore mid-morning on Monday, local time.
The passengers friend said the delay was upsetting.
"[My friend] was tired because she'd watched the Rugby World Cup [final]. She will be tired and grumpy, I would've thought."
Her friend sent her a text at 4am saying the flight had been rescheduled to leave in half an hour.
"She text me: 'Getting ready for 4.30 take-off. Captain is in the cockpit - finally'."
Air New Zealand had revised their timetables as a result of the mix up.
"We have since made a small tweak to our roster timings while the runway work is being done to ensure crew who are required to report close to midnight start a few minutes before 12 rather than a few minutes after, to avoid any possible mix-ups with the date happening again," the spokeswoman said.
"Our team did its best under the circumstances to minimise the disruption to our customers, including carrying out the dinner service and offering customers access to the in-flight entertainment while the aircraft waited on the ground. We apologise for any disruption caused."
This morning's 1.15am NZ282 flight was also delayed, with Auckland Airport confirming the craft did not depart until 3.35am.