While some are angered by the border closure, two suspected cases of COVID-19 were reported on Monday in the NSW border town of Albury.
"One suspected case had recently travelled to Melbourne and had returned prior to hotspot travel restrictions coming into force," a NSW Health statement reads.
The border closure decision was made in consultation with Prime Minister Scott Morrison and NSW Premier Gladys Berejiklian, Mr Andrews said.
The decision marks the first time the Victoria-NSW border has been shut in 100 years - officials last blocked movement between the two states in 1919 during the Spanish flu pandemic.
The closure, which comes into effect at 11:59pm on Tuesday, will be policed on the NSW side, he added.
“We have agreed that the best thing to do is to close the border. That closure will be enforced on the New South Wales side, so as not to be a drain on resources that are very much focused on fighting the virus right now across our state,” Mr Andrews told reporters.
“This is one of those precautionary measures, it is one of those things that I think will help us in broader terms contain the spread of the virus."
Melbourne's coronavirus outbreak intensified over the weekend, with the state recording 108 new cases on Saturday - the twentieth consecutive day of a double-digit rise in daily cases.
Lockdown could last longer
The Saturday spike resulted in a hard lockdown of nine public housing blocks in North Melbourne and Kensington for at least five days.
Mr Andrews said on Monday the lockdowns could last for a fortnight.
“The order was made for 14 days but it can be rescinded earlier than that,” he said.
Of the 127 new cases reported on Monday, 16 are linked to the public housing towers, taking the total number of infections across the nine buildings to 53.
On Monday, Victoria Police said a 32-year-old man had been charged with assault and allegedly trying to leave one of the Flemington towers.
"There was an issue where that male tried to leave against instructions, a fight occurred... that man bit one of the members," Chief Commissioner Shane Patton said.
Some residents and members of the public have criticised the heavy police presence in the nine buildings where many of the residents come from culturally and linguistically diverse backgrounds.
But Mr Patton said the police were there to assist people in quarantine.
"It's about helping the residents of these towers get through this extremely difficult period. We are there to help you, and we will try and work through, and do what we can to make sure things are as peaceful, as calm, and be happy to take questions."
Victoria now has almost 650 active cases of COVID-19.
Mr Andrews apologised for the “inconvenience” the border closure would pose for people who live in border towns, such as Albury-Wodonga.
He said there would be a “permit system” put in place, to be detailed later on Monday, and special facilities set up on the border for people who need to make "unavoidable" crossings.
Ms Berejiklian said closing the border was a “necessary step” given the increase in community transmission in Victoria.
"When our nation had those higher number of cases back in February and March, the vast majority of those cases were from overseas travellers or the direct contacts,” she told reporters in Sydney.
“What is happening in Victoria is very different, which is why we have had to take this necessary step. We wouldn't have taken this step, unless we absolutely had to.”
Ms Berejiklian said there was no reason for other states to close their borders to people from NSW.
“There is really no excuse for any other State, apart from Victoria, to have any border closures with New South Wales and I urge all the other states of Australia, in our national interest, to think about that,” she said.
Queensland Premier Annastacia Palaszczuk welcomed the NSW-Victoria border closure in a statement on Twitter.
West Australian Premier Mark McGowan also praised the decision.
"I'm pleased to hear that common sense has prevailed ... I think it's the smart and correct decision, and I think it is long overdue."
NSW Police Commissioner Mick Fuller said assistance to enforce the border closure has been requested from the Department of Defence.
He said it would be "difficult [but] not impossible" to cross the border in the first 72 hours of the ban. He said exemptions to the ban could be applied for using an online permit system facilitated through Service NSW from Tuesday.
"There will be delays whilst we work through who are essential workers," he said.
"We will take a sensible but pragmatic approach to those coming into New South Wales to ensure we protect the people of New South Wales."
NSW reported 10 new cases of COVID-19 on Monday, none of which came from community transmission.
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