Albury Wodonga Health put in the measures to tackle coronavirus as more information emerged about the only positive COVID-19 case on the Border.

The sufferer flew back into Australia, rather than being overseas on a cruise, before calling ahead prior to having a COVID-19 test at the Wodonga screening clinic.

The 41 year-old did not travel via Albury airport, Murrumbidgee Local Health District director public health Tracey Oakman said.

She said "that person has followed all directions around isolation".

Ms Oakman said more than 700 tests had been done across her area which extends from Hay to Tumbarumba and north to West Wyalong.

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"It is only a matter of time before we have quite a number of cases in our region," she said, given the exponential rate of COVID-19 spread.

Albury Wodonga Health pandemic chief Sally Squire said on Monday that there had now been 251 tests at the service's drive-through clinic in Wodonga.

A second case within the city of Greater Shepparton was revealed on Monday, but North East councils remain coronavirus-free.

Ms Squire said visitor rules were being tightened to protect patients.

The dialysis areas will have no callers allowed, while one guest per patient, aged over 16, will be permitted elsewhere, including maternity.

However, that visitor will need to be the same person throughout the patient's stay.

"We're really asking our community to understand how important this is...how this protects our patients and newborn babies (who) are really amongst our most vulnerable," Ms Squire said.

Northeast Health Wangaratta has restricted maternity visitors to one, with no children or grandparents allowed.

It has also limited public access points to the main entrance, emergency and community care centre.

Similarly, Ms Squire said entrances to Albury and Wodonga hospitals would now be limited to the main doors, apart from emergency patient arrangements.

Visiting hours, which run from noon to 2pm and 5pm to 7pm each day, will be strictly applied.

Visitors will not be permitted if they are unwell, have travelled from overseas in the past two weeks, or have identified as a close personal contact with a confirmed or suspected case.

All visitors will also be asked to wash their hands upon entry as part of infection control.

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