The Murrumbidgee Local Health District has banned anyone who has been in Melbourne in the last 14 days from visiting its facilities.
Victoria has recorded 33 new coronavirus cases in the past 24 hours which are concentrated in several Melbourne "hotspots".
Additional screening requirements for visitors will be put in place across all Murrumbidgee facilities in response, effective immediately.
The screening also applies to staff, who will be required to be symptom-free for 14 days before returning to work, if they have travelled to Melbourne.
MLHD chief executive Jill Ludford.said anyone who had come from Melbourne, including NSW residents, should not attend aged care facilities, hospitals or any other settings with vulnerable people within two weeks of arriving in the region.
"Anyone who has returned from Melbourne and has even the mildest symptoms should be seek testing for COVID-19," Ms Ludford said.
"After the great work that Murrumbidgee residents have done to limit the transmission of the virus, it is critical that we take these precautionary steps to keep our patients safe."
MLHD medical services director Len Bruce said health services would remain vigilant along the Victorian border.
"Our Mobile teams are being deployed to our border towns to increase testing rates in these areas," Dr Bruce said.
"Detecting the virus early is a priority for us in the Murrumbidgee and will help us to take early intervention to stop the spread."
People are reminded to follow the rules around gatherings, maintain physical distance when they are out and about, and wash their hands frequently and thoroughly.
Anyone who feels unwell is invited to call the Murrumbidgee COVID hotline on 1800 831 099 to arrange an appointment at their nearest testing centre, whether that be a clinic or a GP practice.