A team spokeswoman said the decision had been made to save Pallister's energy for the 4x200m freestyle relay which starts on Thursday.
The 1,500m heats start on Tuesday morning at La Defense Arena.
Pallister took bronze in the 1,500m freestyle at the 2022 World Championships in Budapest and was a member of Australia's world-title-winning 4x200m freestyle team at Fukuoka last year.
She is also entered in the 800m freestyle in Paris starting on Friday.
Pallister's blow follows Briton Adam Peaty testing positive for COVID-19 early on Monday, hours after missing out on a third successive gold in the men's 100m breaststroke.
Multiple Australian women's water polo players tested positive for COVID-19 in the days leading up to the opening ceremony, forcing them to isolate from other team members.
The Paris Olympics are being held without strict COVID-19 health protocols, three years after fans were restricted from attending the Summer Games events in Tokyo.
