The council immediately shut the library as a precaution and notified police.

"The council is taking all precautions in line with our pandemic protocols," the council's chief executive Mark Dixon said.

Sources have told The Border Mail the Melbourne visitor was trying to secure a permit to cross the border.

The council is hoping to re-open the library on Monday with staff working at the time sent home.

Council is seeking advice on whether they need to self-isolate for 14 days.

RELATED COVERAGE

Member for Benambra Bill Tilley said the incident was a prime example why the NSW government had imposed tougher border closure measures between Albury and Wodonga.

"The simple solution for NSW to have any confidence in the border districts and Victoria to give any further concession is for Daniel Andrews to lock Melbourne down," he said.

"No ifs, no buts, there is 1.5 million people in regional Victoria suffering for what is going on in Melbourne."

Mr Tilley said his office was aware of another incident where someone from Melbourne, which is in stage three lockdown, had travelled to Wodonga for work purposes.

"The company said they were entitled to come up and work," he said.

"It is insane."