Goulburn Valley Health chief executive Matt Sharp said the person was from the Greater Shepparton region, and was recovering at home in self-isolation.
Mr Sharp said at this time there was "no evidence of a link" between this case and the staff member who tested positive for the virus last week.
"A review into how this staff member became infected with COVID-19 is underway," he said.
The hospital and the Department of Health and Human Services have started and will continue contacting staff and patients who have been in close contact with the confirmed case.
Mr Sharp said staff in close contact had returned negative pathology swabs for the virus but patients would continue to be monitored.
"A very small number of staff who were considered close contacts have been assessed and had pathology swabs taken," he said.
"The results of these pathology tests are negative.
"A small number of patients have been identified through the contact tracing process and they have been reviewed by medical staff.
"These patients will continue to be monitored.
"Follow-up care and treatment has and will be arranged where needed."
Last week, a former Goulburn Valley Health staff member tested positive for COVID-19.
The person was not from the Goulburn Valley area and was believed to be a doctor.
Mr Sharp said a "medium sized number of staff" who had been in contact with this case were tested and had not contracted the virus.
"All staff identified as close contacts and who have had testing for COVID-19 have returned negative results," he said.
Patients who were close contacts were being monitored.
Greater Shepparton reported its tenth case of coronavirus on Sunday, the first increase in more than a week.
"GV Health is continuing to treat inpatients with suspected COVID-19 at Graham St Shepparton," Mr Sharp said.
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