He was shocked there was no vegetarian option on the domestic flight, and said it "beggars belief".
"If Alan Joyce won't change his decision on this, maybe it's time for the Qantas board to take him off the menu," Mr Dee said.
The businessman, who has been flying with Qantas for decades and has always been served vegetarian meals on all of those flights, took to Twitter on Tuesday to express his disappointment.
"I'm on the Adelaide to Sydney flight – I'm informed that #Qantas no longer serve vegetarian food on domestic flights (except Perth)," he tweeted on Sunday.
"The reason I have flown so much with Qantas is because the vegetarian food is always extremely good," Mr Dee told NCA NewsWire.
"The meals always tasted great. Now I'm told on Sunday, 'Sorry, we have nothing for you'. I was hungry, which made me even angrier."
When Mr Dee landed at Sydney Airport just after 10pm, he was further frustrated to find that every single airport food outlet was shut ahead of his two-hour drive back to his home in the Blue Mountains.
He said the "very weird decision" to stop specialist meals for passengers on domestic flights would cost the airline more.
"It's cheaper to buy vegetarian food than meat-based food," Mr Dee said.
"Alan Joyce is charging a premium price for a premium service, but the food isn't as good as Virgin or Jetstar."
Mr Dee, who has been flying Qantas since 1992, said he would give Qantas a few weeks to change its position before switching his allegiance to a different airline.
"I'm going to go to Virgin," Mr Dee said.
"Personally, if this is how Qantas treats vegetarians, they're not going to have my business."
Virgin Australia reached out to Mr Dee via Twitter, reassuring him its airline catered for his needs.
"Hi Jon Dee, we can confirm we do have vegetarian options for our Business and Economy Guests. If you would like more information, please reach out!" they wrote.
A Qantas spokesperson told news.com.au that during Covid the airline made some changes to on-board food and service offerings to "simplify the service delivery for our crew".
"We now offer a single meal/snack option per flight on our shorter flights, such as a chicken pie or a zucchini and onion frittata.
"If the option on a particular flight is not suitable for vegetarians, we try to offer an alternative of a small sweet or savoury snack which is vegetarian."
The spokesperson explained on longer domestic and international flights, customers can pre-book a range of special meals, including vegan and gluten and dairy-free options.