Helen Haines wants to ensure that in preventing a coronavirus health crisis, closing the border does not cause another one.
The Indi MP has called on the NSW government to guarantee Border residents can go to work and access health care across the border as usual.
"This announcement has caused uncertainty for many of us who live in border and neighbouring communities," she said.
"In the past few hours (since Monday's announcement) I've had contact from many people concerned about accessing dialysis and cancer treatment at Albury Wodonga Health's Albury campus.
"There needs to be no doubt in anyone's mind that they will be able to cross the border seamlessly for health issues.
"I don't want to hear of one case where someone on one side of the border is not able to access critical health care on the other because of a health crisis.
"We need guarantees of access and a workable, easily accessible permit system so that people can go to work and businesses can operate."
The NSW government has stated the permit system may not be fully in place for a few days.
"What will happen if someone needs to cross for a medical reason but they don't have a permit? Will they be told to wait a day? The NSW government must clarify how this will work," Dr Haines said.
"It's clearly a serious decision which the NSW and Victorian governments have taken on the latest scientific, health and population advice to keep our communities safe."
Prime Minister Scott Morrison contacted Farrer MP Sussan Ley before the announcement and she said she told him about "the high level of concern and potential impacts this decision will have on our local way of life".
"Quite obviously no one wanted this to occur, but right now state governments need to take the expert health advice to help curb the spread. This is what NSW have done and they've also had to move very quickly," Ms Ley said.
"I expect from here, especially over the next few days, we will need to have a great deal of patience and understanding while NSW puts roadside checks and this permit system in place.
"We're receiving assurances those of us who need to move regularly back and forth across the Murray will still be able to do so."