Security were called to remove the woman, and members of the cabin crew and captain explained what was happening, Mr Murray said.
"They either need to review their [security] protocols or if their protocols actually do say that no one can get on the plane without scanning their barcode, or at least their boarding pass ... then they need to be actually using that policy or enforcing their policy."
Mr Murray, who travels with Air New Zealand about once a month, also said the door of the cockpit was left open while the captain dealt with the situation.
The woman had taken a seat in the front row, he said.
"If you know you've got someone on the plane, who you know is not meant to be there, and she's sitting three feet from the cockpit - it just seems kind of weird to me."
Staff who dealt with the woman were professional and handled the situation well, he said.
The flight departed once all security checks, including whether the woman had any baggage, were completed.
An Air New Zealand spokeswoman said in a statement that the flight was delayed "when it was identified that a person who did not hold a boarding pass for that flight had boarded the aircraft".
"The person was uncommunicative and refused to respond to crew questioning, which resulted in Aviation Security staff being called to remove her."
The woman went through "all normal security screening procedures in order to pass into the departures area of the terminal, including having any luggage x-rayed", she said.
Air New Zealand did not respond to further questions about how the woman boarded the aircraft without presenting a boarding pass.
An Aviation Security Service spokesman said the woman was arrested by police and issued with a trespass notice.
"We did everything we needed to do in terms of screening her. She got through that fine."
Auckland Airport referred all queries on the incident to Aviation Security.
