The passenger then received an email telling them to book another flight at "no additional cost", but staff members told them otherwise.
"The staff tried to tell us that we would have to pay the difference between the new booking and the old one, which was huge," he wrote.
"We had to fight to get the replacement flight refunded."
After finding out their were no flights available that day, staff told passengers they would arrange accommodation for the night, however they only tended to some stragglers, leaving the rest to wander around the airport trying to find rooms to sleep in.
"The first 10 or 15 people get rooms and the rest of us are told that the airline's travel agent is still looking for rooms," they wrote.
"We are told that we can book our own room and that we will be reimbursed up to $150 ... in Queenstown on a Friday night.
"Many of us are at the airport hoping that accommodation comes through up until the airport closes, at 10pm, 6 hours after the cancellation. It never does."
The person writes how disappointed they were with the service of the airline and reveals they see that it is a common issue with other passengers.
"A quick search of news stories this year reveals that this is not an isolated incident," they explain.
"Jetstar's reply to media inquiries associated with previous cancellations suggests that this is part of their business model. For example, when 5 flights out of Sydney got cancelled on the same day, they said '5 out of 400 daily flights is not bad.'
"They are running with such narrow buffers that the slightest disruption can result in cancellations and possibly worse, but apparently this is part of the calculation. Naturally, the time wastage and stress imposed on inconvenienced passengers is not part of the equation."
The passenger explained that they understand that it's a budget airline, but thought that meant they wouldn't get in-flight meals or there would be charges for extra luggage.
"Apparently it also means exposure to a very high risk of cancellations and the resulting chaos that is Jetstar's customer service," they wrote.
The Herald contacted Jetstar, which apologised and explained the reason behind the cancellation.
"We sincerely apologise for the cancellation, which was due to one of our cabin crew members falling ill," Jetstar spokesperson Phil Boeyen said.
"We rebooked passengers on the next available flights to Auckland and assisted with arranging accommodation where required. Passengers were able to request a full refund if they no longer wished to travel."
"We appreciate these cancellations are inconvenient for our passengers and thank them for their understanding," Boeyen continued.
"Jetstar has a very low cancellation rate on its domestic jet services in New Zealand; in the 12 months ended September 2018 the rate was less than 0.8 per cent. Unforeseen issues such as weather, engineering or crewing issues can result in a flight being cancelled."