Passengers flew to Sydney on the first day of the new Trans-Tasman travel bubble yesterday and then took a connecting flight to Melbourne.
New South Wales Premier Gladys Berejiklian said she hoped New Zealand would loosen restrictions on people arriving from Australia soon.
"You haven't spent long in [Melbourne] Airport".
Newstalk ZB's Khalia Strong was at Auckland Airport this morning, where passengers were arriving to board the first flight.
Passengers were required to complete a health declaration, confirming they had only been in New Zealand in the past 14 days, and a health screening upon landing in Sydney.
Mr Andrews said the government is still waiting for Australian Border Force to provide them with the details as to where the passengers are.
However, the incumbent Immigration Minister Alan Tudge announced shortly thereafter that the passenger cards had been handed over to Victoria.
But Andrews, whose Labor Party government is in opposition to the conservative Liberal Party at the helm of the federal government, said he would not get pressured.
"We do not suggest or infer that they did anything wrong", he said.
"There has been something has gone wrong in this system, we are not supposed to be part of this arrangement".
Travellers from New Zealand on "no-quarantine" flights will be able to go to New South Wales, the Australian Capital Territory and the Northern Territory without having to undergo quarantine upon arrival, the authorities said.
"They need to be briefed on those things so they are doing the right thing. Other states and territories may be added at a later date".
When asked if Victoria should consider closing its internal borders, Andrews said he did not want to. "I am not sure that any of them would necessarily need to be tested".
The statistics mean Victoria's coronavirus death count remains at 816 and the national toll is 904.
But overnight Victoria's Department of Health and Human Services (DHHS) confirmed there were 17 passengers, and that the department "does not have legal authority to detain the travellers on arrival". He accused Andrews, who is under pressure to ease a lockdown in Melbourne, of trying to create a distraction, the Australian newspaper reported.
He said the police would visit the passengers later today to check on welfare payments.
New Zealand Flight Centre's head of product Victoria Courtney told Stuff.co.nz that the requirement to quarantine when returning home to New Zealand had caused a "massive deterrent" for travellers to book return tickets.