Victoria on Tuesday recorded an additional 191 new COVID-19 cases.
For businesses on the border, which last closed during the Spanish flu pandemic in 1919, it also poses an immediate logistics headache.
The Transport Workers' Union national secretary, Michael Kaine, who has consistently campaigned for more government support, said the closure of the Victoria-NSW border was bad for Qantas and its smaller, financially stricken rival, Virgin Australia.
McKenzie lives on the NSW side of the river, the boats pick up passengers from the Victoria side and the river itself is classified as part of NSW.
Australia has now recorded nearly 8,800 cases and 106 deaths, far below many other countries, but the Melbourne outbreak has anxious officials.
On Saturday, the Victorian government announced some 3,000 people residing in nine public housing towers in Melbourne would be subject to a "hard lockdown" for at least five days - meaning they can not leave the premises for any reason.
Morrison had previously opposed states closing their borders.
"I wonder if they will need permits", Armstrong said.
There are now 772 active cases in Victoria, with 438 potentially from community transmission.
She has also declared a shut Victorian border would harm Albury-Wodonga, with about 50,000 auto movements between the border towns each day.
Freight haulers, farmers and residents of communities that straddle the border will be able to apply for permits allowing them to cross between the states. Victoria's only other internal border, with South Australia state, is already closed.
The closure of the border is a blow to Australia's hopes of cushioning the fall as the country heads into its first recession in almost three decades.
The sudden spike in cases saw the premier reintroduce lockdown measures at the end of June for residents of 12 postcodes in the greater Melbourne area deemed to be "hot zones".
Health officials last week effectively shut off some 300,000 Melbourne residents to the rest of the city until the end of July, but that has now been extended beyond their neighbourhoods.
When the food arrived it was "at best, questionable pre-packaged meat-like food items that do not look suitable for human consumption".
"Bottom line is no NSW resident should be travelling to Victoria", he said. At least 500 police officers are assigned to the towers per shift.
A spokesman for State Emergency Services told AAP the deliveries had since been returned.
Abdiraham Ibrahim, a father of five living in a Flemington tower said supplies were more accessible on Tuesday.
"People have made the assessment that with it unknown how long the lockdown will go on for, they won't trade through", he said.
Mr Andrews said plans for remote learning had not yet been finalised. They are receiving assistance from Fire Rescue Victoria and the SES.