The Australian airline has been seeking cost savings because of the coronavirus pandemic, which has severely affected the travel industry.
"While it's disappointing to lose a loyal partner, it is understandable," said RA's interim chief executive Rob Clarke.
RA announced in June that it was cutting a third of its full-time staff.
The airline had already said it was losing 2,500 jobs and had posted an annual pre-tax loss of Aus$2.7bn (£1.51bn).
"While we're dealing with this crisis and its aftermath, the cash cost of our sponsorships has to be zero," Qantas chief customer officer Stephanie Tully said in a statement.
"Qantas has had a very long association with Rugby Australia and the Wallabies, and we've stuck with each other during difficult times. Unfortunately, this pandemic has been the undoing."
It said it was stopping cash sponsorship of all sports, but would continue to support Cricket Australia and Football Federation Australia for another year by other means, such as flights and marketing.