The announcement from Football Australia came hours before FIFA's deadline for declarations of interest on Tuesday.
FIFA has already said the tournament will be held in Asia or Oceania, and an Australian bid was seen as the only serious potential challenger to Saudi Arabia, which has already garnered support from the Asian Football Confederation.
A Saudi World Cup is likely to be highly controversial given concerns over the country's human rights record.
It would almost certainly mean another winter edition, as with last year's tournament in Qatar, due to the extreme heat during the region's summer.
A statement from Football Australia said it had "explored the opportunity" of a bid but had decided against it.
"Having taken all factors into consideration, we have reached the conclusion not to do so for the 2034 competition," the statement said.
"Football Australia is ambitious to bring more major tournaments to our shores.
"We believe we are in a strong position to host the Women's Asian Cup in 2026 and then welcome the greatest teams in world football for the 2029 FIFA Club World Cup."
It said hosting those events, in between the 2023 Women's World Cup and 2032 Olympics in Brisbane, would complete a "truly golden decade for Australian football".
Saudi Arabia announced its declaration of interest within hours of FIFA outlining the process for hosting the 2034 tournament.
With the 2026 finals heading to the United States, Canada and Mexico and the 2030 finals to Spain, Portugal and Morocco, including some matches in South America - subject to approval by FIFA's congress - only bids from the Asian Football Confederation and the Oceania Football Confederation will be considered for the 2034 finals.
Saudi Arabia confirmed on October 4 that it would bid for the showpiece tournament in 2034.
Saudi minister of sport Prince Abdulaziz bin Turki Al Faisal said in a statement via the Saudi Press Agency: "Hosting a FIFA World Cup in 2034 would help us achieve our dream of becoming a leading nation in world sport and would mark a significant milestone in the country's transformation.
"As an emerging and welcoming home for all sports, we believe that hosting a FIFA World Cup is a natural next step in our football journey."
Last week Human Rights Watch complained that FIFA was failing to apply its own rules in regards to Saudi Arabia's bid, specifically article seven of its human rights policy.
The article states: "FIFA will constructively engage with relevant authorities and other stakeholders and make every effort to uphold its international human rights responsibilities."
Minky Worden, director of global initiatives at Human Rights Watch, said: "The possibility that FIFA could award Saudi Arabia the 2034 World Cup despite its appalling human rights record and closed door to any monitoring exposes FIFA's commitments to human rights as a sham."
Want a quick and expert briefing on the biggest news stories? Listen to our latest podcasts to find out What You Need To Know...