Police said it was an Islamist-inspired plot, but they did not link the plan to a specific terrorist group.
Australian Federal Police Commissioner Andrew Colvin said officers became aware people in Sydney were allegedly planning to carry out a terrorist attack using an "improvised device."
Turnbull said it was an elaborate conspiracy that involved bringing down an airplane.
The suspects were rounded up in raids in four Sydney suburbs, Australian Federal Police and the New South Wales Police Force said in a news release.
The investigation is ongoing, officials said. Police did not specify the date or location of the threat to Australia's aviation industry.
The suspects are in police custody but have not yet been charged, Colvin said.
"Exactly what is behind this is something that we will need to investigate fully," he said.
The Prime Minister said extra security measures have been in place at Sydney Airport since Thursday and have since been put in place at the country's other major airports.
Transport security officials advised travelers to get to their airports two hours before their scheduled flight departures.
"Those traveling should go about their business with confidence," he added.
Australia's terrorism threat level remains in the middle at "probable," Turnbull said, between "possible" and "expected."
Last month, ISIS claimed responsibility for an attack at a suburban Melbourne apartment building where one man was killed and three police officers were wounded.
The attacker, who was known to police and out on parole, was shot dead after he ended a standoff by bursting out of an apartment.