The man, aged in his 30s, returned to Australia on April 19 from overseas and undertook hotel quarantine in South Australia.
He then travelled to Victoria, returning to his home in Wollert, in Melbourne's north, on May 4 before developing symptoms on May 8.
He was tested on Monday, May 10, before returning a positive result on Tuesday morning, before being retested again, with another positive result.
The man is currently isolating at home.
Victorian Health Minister Martin Foley said the man's three household contacts had all tested negative.
Four tier one exposure sites have been linked to the new case.
Anyone who has been to these sites must get tested and isolate for 14 days:
● Altona North, TIC Group (front office) at 232 Blackshaws Rd, all day on Thursday, May 6.
● Melbourne CBD, Curry Vault Indian Restaurant, 18-20 Bank Place, between 6.30 pm and 9.30 pm on Friday, May 7.
● India Gates Spices and Groceries, at 560-590 High St, Epping, between 5 pm and 6 pm on Saturday, May 8.
● Epping Woolworths, corner of Cooper and High Sts, between 5.40 pm and 6.30 pm on Saturday, May 8.
Anyone who has attended the following tier two sites must also isolate, get tested and remain in quarantine until they receive a negative result:
● 7-Eleven at 705 High St, Epping, between 6.30 pm and 7 pm on Thursday, May 6, and between 11.10 am and 11.40 am on Saturday, May 8.
● Altona North, TIC Group (rear warehouse) at 232 Blackshaws Rd, all day on Thursday, May 6.
Victorian health authorities are also working with interstate counterparts to determine the likely source of this infection.
South Australian chief public health officer Professor Nicola Spurrier said the new case had quarantined in a medi-hotel next door to a traveller who tested positive for COVID-19 on May 4.
Genomic testing will be conducted to determine if there is a link.
Prof Spurrier said there was also a possibility the man may have caught the virus overseas and had a long incubation period before becoming symptomatic.
However she said the man did not appear to be contagious while in South Australia.
The individual had tested positive to the virus while in hotel quarantine.
Anyone with symptoms of COVID-19 including fever, cough, sore throat, runny nose, chills or sweats or a change in sense of smell or taste must be tested immediately.
To see where to get tested, visit coronavirus.vic.gov.au/where-get-tested-covid-19
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