The coronavirus, which is believed to have originated in a wildlife market in the central Chinese city of Wuhan, has killed 80 people, all of them in China, and infected more than 2,700, the vast majority in China.
The woman traveled on a direct flight to Sydney from Wuhan and developed symptoms within 24 hours and went to an emergency department, New South Wales Chief Health Officer Kerry Chant told reporters.
"The patient was immediately put into isolation," Chant said.
Officials were tracing "a couple of very low-level contacts" related to the woman, Chant said.
Australia's first four cases were confirmed on Saturday, with one in Melbourne and three in Sydney, with health officials saying they were expecting more, given the volume of travel between Australia and China.
Australian officials said on Monday they are working with Chinese authorities on how to evacuate about 100 Australian children and young people out of Wuhan.
"We are working on a number of fronts, firstly to make sure ... that there is support for those Australians and we are also working on, as are other countries, to try to secure their ability to return to Australia," Health Minister Greg Hunt told Australian Broadcasting Corporation Radio on Monday morning.
Foreign Minister Marise Payne told the 3AW talk radio that the government did not have a "definite" number of Australians in Wuhan, or in Hubei province, as there were a significant number with dual citizenships, some of whom may not have traveled on Australian passports.