People who have travelled to Melbourne and are scheduled for non-urgent surgery at Murrumbidgee Local Health District services may have their procedures postponed.
Public health director Tracey Oakman said a number of MLHD staff had also been asked to not work for a fortnight after being in Melbourne.
"I think we need to be really careful now, with the cases that we're seeing in Melbourne," she said.
"We're asking people who come into our facilities if they've been to Melbourne in the last 14 days.
"If they are a visitor, we may ask them not to attend our facility.
"For patients, if anyone needs care, they will certainly be given the care, but there may be postponement of some non-urgent elective surgery for a couple weeks while they are in that incubation time-frame.
"Our staff are the same; if they have been to Melbourne, we ask that they not work in our clinical areas ... for the period of 14 days."
Ms Oakman said staff had complied with the request.
"I have had no negative feedback from staff members who have been asked to either not work or work from home," she said.
"People are reasonable, and our staff members understand we're trying to stop the spread of COVID.
"We're taking the outbreak in Melbourne very, very seriously.
"We do ask you not to travel to Melbourne, if you can avoid that."
MLHD environmental health teams have visited NSW ski fields in the district to ensure businesses have COVID-19 plans in place.
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Mobile testing vans are also visiting areas along the NSW-Victoria border this week, including Mulwala, with Ms Oakman advising people not to travel to Melbourne during the school holidays.
"There's lots of border testing being done in this next week," Ms Oakman said.
"There's a whole range of areas the testing van is going to, to try and capture anyone who may be symptomatic who hasn't had the opportunity to be tested.
"Anyone who has symptoms - please don't hesitate and get tested immediately."
There have been no new cases reported in the Murrumbidgee Local Health District.
A total of 18,608 tests have been completed, an increase of 2423 since last Monday.
Anyone with symptoms should call the COVID-19 Hotline on 1800 831 099.