The total number of confirmed cases in the country today is 2,317.
The Ministry added that anybody who has travelled from Melbourne need to get a test and self-isolate at home or in the accommodation they are staying in until they have a negative result.
As for the results of those who have been tested, as of this morning, 2,350 travellers and 178 air crew had returned negative tests.
Officials were continuing to follow-up travellers who were still waiting on test results.
Testing records were being matched with passenger departures and the Ministry expected to be able to provide a fuller picture on numbers tomorrow.
Under the current Section 70 notice, travellers weren't allowed to return to Melbourne until they had returned a negative result.
Anyone who has been in Victoria since May 11 also needed to keep checking the Victorian Government website as locations of interest were continually being added.
The Ministry reminded travellers that not everyone in the group of 4539 would be tested in New Zealand - there were about 1200 known to have already returned to Australia, while others were infants who were not required to be tested.
If they had been to a location of interest people can call Healthline on 0800 358 5453 for further information.
The ministry said the variant of Covid being found in Melbourne is the B.1.617.1 variant which was first reported in India. It is considered more infectious than the original variant.
"The typical symptoms to look out for include a new or worsening cough, fever (at least 38C), shortness of breath, a sore throat, sneezing and runny nose and/or temporary loss of smell," the ministry said.
"Some people may present with atypical symptoms, with or without typical symptoms. These include new onset of fever, diarrhoea, headache, myalgia (muscle pain), nausea/vomiting, confusion/irritability."
The Melbourne cluster reinforced the importance of people in New Zealand keeping a record of where they have been by scanning QR codes or keeping a manual diary of their movements. It gave contact tracers the ability to quickly find potential close and casual contacts if there was a positive Covid case here.
Yesterday, there was one new Covid case in managed isolation when a person returning from India tested positive on day one of routine testing.
In Australia meanwhile, Victoria health officials were scrambling to trace a "mystery case" at a Melbourne aged-care facility.
One of the state's five new Covid cases yesterday was a worker at an aged-care facility in Melbourne's west.
Health authorities were trying to determine how the female healthcare worker at Arcare Maidstone, who lives in Altona, caught the virus.
