The woman was in her 70s and had underlying health conditions.
The Cobram-Barooga region experienced at least seven confirmed coronavirus cases since Wednesday with the Berrigan Shire rising from one to five.
Neighbouring Federation Shire saw growth slow, going from six cases to seven.
No information has been released about where in the municipalities the people reside or their prior movements.
A total of 2139 people have been tested for COVID-19 across the Murrumbidgee Local Health District.
MLHD reported five people in its authority have recovered from COVID-19 and only one person has died from the virus.
More than 1160 people have tested positive in Victoria for COVID-19 with more than 210 cases in regional Victoria.
The full testing criteria list is available on the state health department's website.
All travelers returning from overseas to Victoria will be placed in enforced quarantine for the self-isolation period of 14 days.
Police officers have strong powers to enforce these directions and can issue on the spot fines, including up to $1652 for individuals and up to $9913 for businesses.
Under the State of Emergency, people who do not comply could also be taken to court and receive a fine of up to $20 000. Companies face fines of up to $100 000.
More information is available at www.dhhs.vic.gov.au/coronavirus
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