The evacuees were first sent to specially quarantined facilities at a remote airbase in Western Australia.
The Qantas 747 touched down last night (NZ time) at a Royal Australian Air Force base about 1200km north of Perth, carrying 243 passengers, 14 crew, four pilots and officials from the Department of Health.
Several children were on board, with 89 evacuees under 16 years of age, including five under the age of two.
The 747 could not land at the small Christmas Island airstrip, so the passengers will be transferred to two smaller planes to make the trip.
A chartered flight left the Learmonth base about overnight (NZ time), bound for Christmas Island.
A Royal Flying Doctor Service (RFDS) flight has also left Learmonth.
A spokeswoman for the WA Department of Health said a patient had been transported to Perth but the decision to do so was not related to the coronavirus.
The patient had a condition that made it necessary for them to be close to a tertiary hospital, the spokeswoman said, and they would be kept in home isolation following the appropriate protocols.
WA chief health officer Andrew Robertson said earlier that it was unlikely any passengers would have developed an illness or coronavirus symptoms during their flight from Wuhan.
"They were not allowed on the plane if they were unwell," Dr Robertson said.
"Probably the more likely scenario is that there are other medical conditions that require treatment that we will have to bring back to Perth."
WA Health Minister Roger Cook had also said any passengers deemed too sick to travel to Christmas Island would be flown to hospital in Perth by the RFDS.
The flight out of Wuhan is the first of two that will take several hundred Australian citizens and permanent residents out of the locked-down city.
Once on Christmas Island, they will spend two weeks in quarantine at the almost-empty immigration detention centre with a team of doctors and nurses.