Goulburn Valley Health chief executive Matt Sharp said a "medium sized number of staff" had been tested and did not contract the virus.
"All staff identified as close contacts and who have had testing for COVID-19 have returned negative results," he said.
"These staff have been contacted regarding their results."
He said a "very small number" of patients who were considered close contacts have been reviewed by medical staff, and would be observed.
"These patients are stable and will continue to be monitored," Mr Sharp said.
"These patients are not currently showing signs of COVID-19 infection.
"Our priority remains the health and wellbeing of GV Health’s patients and staff."
He confirmed contact tracing by the Department of Health and Human Services was completed at the weekend.
Mr Sharp said the staff member who tested positive was employed at the hospital's Graham Street Shepparton campus in early April on a temporary basis.
The person, who is now recovering at home and in self-quarantine, experienced COVID-19 symptoms following the completion of their last shift at GV Health.
Mr Sharp said the staff member was not from the Goulburn Valley region.
It is believed the person is a doctor.
The chief executive assured patients should not change their plans to attend appointments at the hospital.
"Patients should not cancel or postpone any appointments or not attend GV Health to access health care services and/or treatment," Mr Sharp said.
"All necessary precautions have and will continue to be taken."
Greater Shepparton has recorded its tenth case of coronavirus, the first case reported in the region in more than a week.
GV Health is continuing to treat inpatients with either confirmed or suspected COVID-19 at Graham Street Shepparton.
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