Andrews announced the closure at a press conference this morning where he said Victoria had recorded a further 127 new coronavirus cases and a man in his 90s had died in a Victorian hospital.
He said the decision to close the border followed talks with NSW Premier Gladys Berejiklian and Prime Minister Scott Morrison.
The three leaders agreed closing the border would be the "smart call" at this point in time, Mr Andrews said.
"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 said.
The closure will take effect from 11:59pm on Tuesday.
The decision followed a weekend that saw Victoria record 108 new cases on Saturday - the second highest increase in the state in a single day since the pandemic began - and lock down nine public housing estates in inner Melbourne in a bid to contain an outbreak of the virus.
Another 74 coronavirus cases were recorded in the state yesterday.
The Premier said that of today's 127 new cases, 16 were detected in the public housing towers that had been locked down.
An additional 10 infections from earlier numbers had been linked to the towers, bringing the total in the outbreak to 53 cases.
"It's essentially a doubling of the numbers since yesterday," Chief Health Officer Brett Sutton said.
Andrews said there would be a permit system for people who needed to cross the NSW border.
"There will be a facility for people who live on those border communities to be able to travel to and from for the purposes of work, the purposes of the essential health services they might need," he said.