"He did not display symptoms on his flights to Melbourne and there are no close contacts or casual contacts in the public to follow up at this time," Victoria's Chief Health Officer Professor Brett Sutton said in a statement on Wednesday morning.
Meanwhile, in NSW, a woman in her 50s who has not recently travelled overseas became the third confirmed example of community-transmitted coronavirus in the state.
NSW Health has also moved to alert passengers who were on four separate flights from Asia over the past week as five people tested positive for the virus after arriving in Sydney from overseas.
Two men in their 30s had travelled from Iran, a man in his 50s had recently returned from Singapore, a woman in her 60s had been in South Korea and a second woman in her 60s had travelled from Japan.
Of the new batch of cases, the first arrived in Sydney on 1 March after transiting through Malaysia and Singapore. The man, who had previously been in Iran, flew on Jetstar Asia Airways Flight 3K686 from Kuala Lumpur to Singapore, before transferring to Qantas Flight QF82.
Shortly after, the eleventh case was identified as a man in his 50s, who travelled to Sydney from Singapore on Qantas Flight QF02 while experiencing symptoms. He arrived in Sydney on 28 February.
The other affected flights are: Korean Air KE121, which arrived in Sydney from South Korea on the 27 February, and Malindo Air OD171, which arrived in Sydney from Kuala Lumpur on 1 March.
NSW Health has not released details of the flight the woman in her 60s took when she landed in Sydney from Japan on the 21 February.
"Reflecting what is happening worldwide, and obviously an increasing number of people are being diagnosed with the coronavirus, what we are now seeing in Sydney, in NSW is reflective of that situation," NSW Health Minister Brad Hazzard told reporters on Tuesday.
"We are seeing quite an escalation of diagnosis of the virus."
Health authorities are also advising passengers who sat near a coronavirus-infected woman on a Doha-to-Sydney flight to immediately isolate themselves at home.
A woman in her 50s flew into Australia from Iran on 23 February aboard Qatar Airways flight 908 from Doha.
She developed symptoms of COVID-19 the next day and was tested on Saturday after attending a hospital emergency department.
NSW Health on Tuesday said the airline had passed on the infected passenger's seat details as well as the names of those sitting nearby.
The health authority is now urging adjacent passengers - seated two rows in front and behind seat 43H - to self-isolate and contact their local GP or public health unit.
The spike in cases comes after NSW authorities confirmed the first cases of locally-acquired coronavirus on Monday, including a 53-year-old doctor from Sydney's Ryde Hospital who had not recently travelled to affected countries.
The doctor is in a stable condition at Westmead Hospital and "going quite well", Mr Hazzard said on Tuesday.
Forty staff members of Ryde Hospital - including 13 doctors, 23 nurses and four other health workers - have been instructed to isolate at home after being identified as having had close contact with the infected doctor.
A further eight patients of the doctor are showing no symptoms, while 29 other patients identified as casual contacts are being contacted, authorities said.
"We are making sure we get in contact with them and make sure they don't have symptoms," Mr Hazzard said. "It's a bit of a worry."
The doctor was not treating any confirmed coronavirus patients and it unclear where he contracted the virus.
Another locally-acquired case in Sydney is the 41-year-old sister of an infected man who recently returned from Iran, where the virus has so far infected at least 2,300 people.
Additional reporting by AAP.
A previous version of this article incorrectly stated that Qatar Airways flight 908 departed Dubai.