The state's health department said the new case was a primary close contact of an existing case and they had been in quarantine throughout their infectious period.
Investigations into the acquisition source of the positive Reservoir family of four and the Melton couple who travelled to Queensland - all genomically linked to the Kappa variant - are continuing. Contact tracing has identified more than 15,000 close contacts.
They were caught at the border and tested negative for the virus.
New Zealand citizens, permanent residents, people with humanitarian exemptions and critical workers will still be able to take green zone flights to New Zealand from Melbourne - but will need a negative pre-departure test within three days of departure.
Western Australia reclassified Victoria as a "low risk" state from 6pm Friday, but Victorians making the trip will still need to isolate for 14 days.
A fresh warning was today issued for Kiwi travellers to these states after the couple breached the city's lockdown.
Queensland declared Victoria a coronavirus hotspot from 1am on May 28.
The Ministry of Health has announced there is one new case of Covid-19 in managed isolation, and none in the community.
Neighbouring New South Wales (NSW) state and Queensland, meanwhile, are on virus alert after an infected woman and her husband travelled from Victoria through several country towns in both states.
More than 400 people who visited the listed exposure sites at the relevant times have also come forward to Queensland Health.
Those who have been at a location of interest at the specified times are not allowed to travel into New Zealand within 14 days of exposure.
Queensland Health reported two cases of COVID-19 on Wednesday in the Victorian couple, who had driven from Victoria to Queensland's Sunshine Coast.
There were two new cases of Covid yesterday and one person with coronavirus is being treated at Middlemore Hospital after being transferred from the Jet Park Hotel MIQ facility overnight on Monday. "This case has done all the right things from our initial interviews, the individual recognised that they had symptoms, got tested and had a test result all within the same day", Mr Foley said.
It's understood they were permanently moving to Queensland, where the husband was due to start a new job.
But Director-General of Health Dr Ashley Bloomfield also said three people had arrived in New Zealand in breach of the lockdown restrictions, flying from Melbourne via Sydney last week.