He arrived in Melbourne on Sunday on a 5.30pm flight from Sydney and caught public transport home from the airport.
The man began showing symptoms about 10pm on Tuesday and was tested on Wednesday.
Authorities say both men are being interviewed and a full public health response is under way. Their cases will be recorded in tomorrow's coronavirus tally.
The second man's family are now in isolation and are also being tested, while the dry-cleaning business is closed for deep cleaning.
QR code data from the business is being analysed by authorities so more contacts can be identified, the Department of Human Services and Health Victoria has confirmed.
The other local case recorded earlier on Thursday was a known primary close contact linked to the Kings Park apartment complex. That person has been quarantining throughout their infectious period.
Three cases were also acquired from overseas, all of which are in hotel quarantine.
Victorian Health Minister Martin Foley said given the patterns of the Delta variant spreading around Sydney, the state government was taking a "conservative approach" and working on the basis the man had the same strain.
"This is a rapidly developing situation in NSW and we are acting quickly to make sure that Victoria stays secure and safe to the threat that is posed by this Delta variant," he said.
Foley said the public health team acted quickly and had already established his primary close contacts.
Victorian Covid-19 response commander Jeroen Weimar said he understood the man had not yet been contacted by NSW contact-tracing authorities, despite the social event he attended being the subject of inquiries there.
"The reasons for that we'll work through in the coming hours," he told reporters.
Weimar said the store where the man worked had a QR system in place and it had closed for cleaning.
Victoria has extended the number of red zones in NSW, declaring all of Greater Sydney and Wollongong red zones from 1am Friday.
Police were ramping up patrols on the Victoria/NSW border, the government warned.
"This is not a time for selfish behaviour. Anyone who puts the health and safety of the Victorian community at risk will be held to account by our authorities and that includes substantial fines," Foley said.
He said the travel advice was clear – Victorians could not to fly into a red zone.
Individuals from other states who've been in a red zone are also barred from entering Victoria.
"If you try to enter Victoria at an airport, you can be fined and you will be sent back. You may indeed have to stay in hotel quarantine if there's no return flight for you at that time," he said.
"If you're a Victorian … and been in a red zone that's come into effect, you can get a red zone permit, but you have to be tested and you have to quarantine for 14 days."
Despite the latest two cases, an easing of restrictions in on track for Victoria at 11.59pm Thursday.
Under the changes, crowds will return to community and professional sport, there'll be an increase of people allowed at indoor and outdoor gatherings and an increase of patron caps at hospitality venues.
However, masks must still be worn indoors.
The recommendation for face masks to be worn outdoors where 1.5m social distancing can't be maintained also still applies.
Dance floors at weddings and nightclubs was another restriction that was unchanged, with nightclubs and karaoke venues only able to open for seated service.
Melburnians can return to offices up to 75 per cent capacity or 30 people per workplace and the cap on spectators at community sport will be 1000.
Theatres will initially open at 50 per cent capacity, with up to 1000 people, and this weekend crowds can attend public events and outdoor stadiums with a limit of 50 per cent or up to 25,000 people.
Another easing of restrictions has also been flagged for July 1, taking Victoria back to the settings it had before the outbreak started.
