Victoria Premier Daniel Andrews says officials have "absolutely no power" to detain the 17 travellers from New Zealand who arrived in Melbourne via Sydney last night.
The passengers flew to Sydney yesterday, on day one of the new trans-Tasman travel bubble, then caught a connecting flight to Melbourne.
Passengers from New Zealand now do not need to quarantine upon arriving in New South Wales, but Victoria was not part of the bubble arrangements.
Andrews said the 17 passengers left Melbourne Airport within minutes of arriving last night.
"Our officers have absolutely no power to stop someone, to detain someone in those circumstances, particularly given they were coming from a very low-virus part of the world," he said today.
Andrews said Victorian officials were still waiting to get the passengers' arrival cards from the Australian Border Force.
"Because we don't have the cards, I can't tell you whether they are New Zealand or Australian citizens," he said.
"They could be Victorians for all we know."
However shortly afterwards, Acting Immigration Minister Alan Tudge said the passenger cards had been handed over to Victoria.
Andrews said it was also unknown whether the people who arrived knew about the restrictions in place in Victoria.
"We're not asserting or inferring that they have done anything wrong," he said.
"There has been something has gone wrong in this system, we are not supposed to be part of this [travel bubble] arrangement."
The Premier said he had written to Prime Minister Scott Morrison to try to make sure more arrivals did not travel to Melbourne on Sunday, when more flights from New Zealand are due to arrive.
"I don't fire off letters to the prime minister unless there is a need to make things formal," he said.
"And our formal position, which hasn't changed, is we are not ready to accept people into our state from other countries, even New Zealand."
Victoria has not accepted international arrivals since early July.
Victoria's Department of Health and Human Services (DHHS) said its authorised officers did not have legal authority to detain travellers on arrival.
Police Deputy Commissioner Rick Nugent said the passengers were in Melbourne and not under any detention orders.
He said police would visit the passengers later today for welfare checks.
New Zealanders travel to Australia
In a statement, Australian Border Force said "domestic border restrictions are a matter for states and territories".
But the Australian Department of Home Affairs says on its website that "quarantine-free travel from New Zealand will initially be to New South Wales and the Northern Territory only. Other states and territories may be added at a later date."
A spokesperson from the New Zealand Ministry of Foreign Affairs and Trade (MFAT) said: "The Ministry of Foreign Affairs and Trade is aware of media reports, but we have not been approached in relation to this matter."
Three flights from New Zealand touched down at Sydney Airport earlier on Friday carrying international passengers who, for the first time in seven months, will not need to quarantine upon arrival.
At Sydney Airport there were tears and hugs as loved ones reunited, with many passengers flying one-way.
NSW Health Minister Brad Hazzard described it as a "great day", but pointed out New Zealanders arriving on Friday would need to prove they are symptom-free and satisfy other health requirements.
There will be a total of 16 flights between the two countries each week, with Jetstar and Qantas joining Air New Zealand and Qatar Airways in advertising the trans-Tasman flights.
In a media statement yesterday, Air New Zealand said fares beyond Sydney were not able to be booked via the airline due to Australian state restrictions.
"Passengers planning to travel interstate beyond New South Wales will need to ensure they have checked state and territory travel restrictions and have the appropriate exemptions/approvals to travel as these continue to change," the statement said.
Announcing the travel bubble arrangements earlier this month, Deputy Prime Minister Michael McCormack said to start with, visitors to Australia could only go to New South Wales and the Northern Territory.
McCormack said that was because both jurisdictions impose travel restrictions on places in line with the Commonwealth's definition of a hotspot - a place with a three-day rolling average of three locally acquired cases per day.
Visitors from New Zealand are only allowed to visit if they haven't been to a designated hotspot in the last 14 days.