Two staff from the North-West Regional Hospital have tested positive to coronavirus.
Chief medical officer, Professor Tony Lawler, said on Friday night that the two workers were among six new cases confirmed on Friday.
"An investigation has begun immediately into identifying and contacting any person who has had close contact with either of these two staff, both inside and outside of the hospital," Professor Lawler said.
"The Tasmanian Health Service has moved immediately to establish an Incident Management Team, and will work to ascertain any people who may be at risk of being exposed to coronavirus at the hospital and ensure necessary actions are taken.
"While it may be necessary for other staff and patients to be tested for coronavirus, this will occur as investigations progress.
"We will assess and test any patient or staff member who is determined to be at risk of coronavirus and ensure the highest standards of care continue to be provided at the hospital.
"We acknowledge this situation may cause some concern. The safety of our patients and our dedicated staff remain our highest priority, and neither the hospital's operations nor patient services have changed at this time."
Professor Lawler said patients, staff and the public would be kept informed of the situation as the investigation progressed.