ERH chief executive Nick Bush said the Echuca resident was tested at the hospital’s special facility set up in anticipation of the virus’ spread.
"She presented to ERH on Saturday as she had been overseas," he said.
"She has no symptoms, so she is otherwise well and is self-isolating."
While Mr Bush said the woman came straight to the hospital, the health department was following up with people who may have been in contact with her.
"They are managing family members or others in contact with her and managing the external spread in the community," he said.
ERH's first case of coronavirus was a Moama man who had returned from the US last week.
After being tested when presenting at the hospital’s emergency department with an upper respiratory condition, the man in his 40s had gone straight into self-managed isolation where he remains.
“The staff have been well prepared in managing these presentations and all care was taken for the patient and our team,” Mr Bush said.
Mr Bush said 130 patients had presented to the coronavirus screening clinic as of today, with 66 meeting the test criteria.
"Two have come back positive," he said.
"The test takes about two to three days to come back, so we're awaiting 10 to 15 tests at any one time."
The Victorian Health Department has said the public can be confident that all close contacts will be identified and responded to accordingly as required to protect public health.
“As part of our contract tracing, any public exposure sites are contacted and provided with advice about the transmission risks and any cleaning that may be required," a spokesperson said.
“The Department of Health and Human Services does not identify individual cases or their close contacts.
“DHHS also needs to ensure patient confidentiality and work to minimise stigmatisation and discrimination around COVID 19.”
Mr Bush encouraged people to continue washing their hands and keeping a safe distance between themselves to prevent the spread of COVID-19.
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