Migrants also tried to break out of the Villawood camp, police said, in the latest of a series of violent incidents to hit the country's centres for asylum seekers.
Security is being increased at the camps in Australia and at a centre on Christmas Island, where detainees had an angry stand-off with guards.
Refugee advocates say the trouble stems from desperation among migrants, who may be held for years while their claims for asylum are processed.
Prime Minister John Howard has said the protests will not alter his government's policies.
There have been protests and fires at the Woomera and Baxter detention centres in South Australia, Port Hedland in Western Australia, as well as Christmas Island and now Villawood.
Immigration officials said about 20 mainly Chinese migrants broke windows at the Villawood camp to steal keys to a staff car.
Some then tried to use the car to ram their way through perimeter gates but were blocked by a police vehicle.
Criminal investigation
Elsewhere in the camp, other detainees set buildings on fire causing damage estimated at about US$270,000, officials said.
"This was criminal damage of the worst kind - a rampage intended to cause destruction with no regard for the safety of the other detainees housed at Villawood," an immigration spokesman said.
He said security had been stepped up at all detention centres in Australia and federal police were investigating the blazes with a view to laying criminal charges.
The Refugee Council of Australia believes a fear of indefinite detention is the main factor behind the disturbances.
The BBC's Phil Mercer in Sydney says the processing of asylum claims usually takes a few months, but it is not uncommon for some detainees to be held for up to three years while awaiting a final decision.
Mr Howard acknowledged the unrest but said his government would not be deterred from detaining illegal immigrants or from diverting boats carrying mainly Afghan and Middle Eastern asylum seekers to Pacific islands.
Both policies have been criticised by human rights groups and the United Nations.