Sarah Hort arrived at Potts Point post office on Wednesday for an appointment she made online more than two weeks ago.
The 23-year-old had received a text on Tuesday from Australia Post, confirming her midday appointment to renew her passport.
But to her surprise, the doors were locked.
She tried to call Australia Post's help and support line but couldn't get through. The automated reply announced businesses were "closed due to the public holiday".
Ms Hort said she couldn't understand what was happening, as Wednesday wasn't a public holiday.
"Even if it was, why would they schedule appointments knowing no one would be there?" she said.
Ms Hort then called the Australian Passport Office, which told her the Martin Place post office was open and was taking new passport and renewal applications.
A long queue snaked out of the Martin Place office, with some people saying they had waited more than two hours to be served.
The Australian Passport Office says people should allow approximately three weeks when applying for a new passport, while for urgent applications they can request priority service that costs $127 and ensures the passport arrives within two business days.
Ms Hort's planned trip to New Caledonia is in early February, but other people in the Martin Place queue on Wednesday were facing greater challenges.
One 21-year-old man, who asked not to be named, said: "I don't think I'll make it by the 1:30pm cut-off, and then they'll consider it an extra [business] day ... the line is too long and the people in front of us have been waiting over an hour.
"If I don't make my flight to Lebanon on Saturday, I can't go to the mass funeral for my father," he said.
This year, December 28 was the annual Australia Post authorised holiday. An Australia Post statement said the holiday has been enjoyed by staff for more than 50 years to recognise the hard work put in by the workforce throughout the year.
Some post offices were open, such as the one at Martin Place, but there were no deliveries.
"This year was one of our busiest festive periods ever – from October we have been successfully delivering more than 1 million parcels a day and in early December we broke a record, delivering more than 2 million parcels in a 24-hour period," the statement said.
"We alert our customers about our annual authorised holiday in advance via public notices in our post offices and our website."
A spokesperson said Australia Post would try to contact Ms Hort to organise an appointment for her on Thursday morning.
Australia Post holiday trading & delivery
December 28: Australia Post authorised holiday: Post Offices open (selected only), no deliveries
December 29: Post Offices open, delivering
December 30: Post Offices open, delivering
December 31: Post Offices open, no deliveries
January 1: New Year's Day: Post Offices closed, no deliveries
January 2: New Year's Day public holiday: Post Offices closed, no deliveries
January 3: Post Offices open, delivering