Local residents are expected to be allowed to cross the river for legitimate reasons but will need to apply to Service NSW to do so.
It is understood they will not be required to self-isolate for 14 days once returning to NSW and a 3564 postcode license will see them waved through.
But the NSW Police have warned the next three days will be challenging for those crossing the border as one of the main check points is created at Moama.
The Cobb Hwy has been listed as tier A - the highest grade of crossing - meaning a strong police presence and potentially members of the military will be based at Moama.
NSW Police Commissioner Mick Fuller said border communities such as Echuca-Moama had to be treated differently than the rest of the state.
"There needs to be a sensible bubble around those border towns,” he said.
"That bubble, or those postcodes, will be seen differently to other Victorians.
"We'll make it easier for those to travel across. They will need to apply for a simple exemption and that will see them through this crisis."
It comes in the aftermath of a dramatic 48 hours which has seen the border between NSW and Victoria closed for the first time since the 1919 Spanish Flu Pandemic.
NSW residents will not be stopped from entering Victoria, however will be required to apply for an exemption to return, and may be required to self-isolate for 14 hours.
However there is light at the end of the tunnel for those in Echuca, with Mr Andrews suggesting restrictions may soon be eased in regional areas.
"I hope very soon to be able to be before you again talking about further easing of restrictions in regional Victoria. That's not for today,” he said in a press conference on Tuesday.
"I do hope that is quite soon. And we'll only be able to achieve that if we continue to contain within metropolitan Melbourne and not see large outbreaks or additional cases in regional Victoria."