Three primary household contacts of the man have tested negative for coronavirus, the state government confirmed.
Health minister Martin Foley and chief health officer Brett Sutton briefed the media on Tuesday afternoon.
He said a secondary test had confirmed the man, aged in his 30s, had returned a second positive test.
Mr Foley announced three 'tier one' exposure sites linked to the man - a curry restaurant in Melbourne's CBD and two stores in the outer northern suburb of Epping, including a Woolworths supermarket.
"Contact tracing is well underway," Mr Foley said.
Mr Foley said work was being done to establish when the man was infectious, and whether that was during his flight back to Melbourne from Adelaide after a stint in quarantine.
The man had returned to Australia from India, via the Maldives and Singapore, Mr Foley said.
Mr Foley used the case as a chance to promote the benefits of vaccination.
"This case is a reminder that we are still in the grip of a global pandemic."
Mr Sutton said no changes were planned to current coronavirus restrictions in Victoria.
"We're not foreshadowing anything," he said. "The good and recommended advice is good advice for all times. People should wear masks if they can't physically distance from others, especially in indoor settings.
"People should also check in with QR codes."
A NEW community COVID-19 case has been reported in Victoria, in a man who recently left hotel quarantine in South Australia.
The man tested positive for COVID-19 on Tuesday morning, after being swabbed on Monday May 10. He developed symptoms on May 8.
The man had returned to his Woollert home on May 4, after quarantining in South Australia on return from overseas.
The Department of Health confirmed a full public health response was underway while it arranged further testing to confirm the diagnosis.
The department confirmed the man in his 30s was being interviewed to verify exposure sites. It said these would be published when confirmed.
The man is isolating at home, as are his household primary contacts, who are also being interviewed and will be urgently tested.
The department said it was working with interstate counterparts to find the likely source of the COVID-19 infection.
It urged anyone to get tested immediately if they had symptoms of COVID-19 such as fever, cough, sore throat, runny nose, chills, sweats, or a change in sense of smell or taste.
A full list of testing sites is available online at: dhhs.vic.gov.au/getting-tested.
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