Two staff at the North-West Regional Hospital are among the state's latest confirmed coronavirus cases.
Chief medical officer, Professor Tony Lawler, confirmed on Monday night that a further two staff members had tested positive for coronavirus.
He said they were among three new cases confirmed in the state on Monday.
"This takes the number of staff who have tested positive for coronavirus in this outbreak to six. An inpatient has also previously tested positive," Professor Lawler said.
"An Outbreak Management Team is already identifying and contacting any person who has had close contact with either of these two staff and will ensure necessary actions are taken.
"If any staff member or patient is determined to be a close contact of these cases, they will be contacted and advised of what action they need to take.
"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 staff member who is symptomatic and any patient who is symptomatic and determined to be at risk of coronavirus."
Professor Lawler said the health service acknowledged the current situation was creating concern, both for staff and for the community.
"We are taking every action in accordance with best advice to ensure possible contacts are identified as quickly as possible. The safety of our patients and our dedicated staff remain our highest priority, and there may be some disruption to normal hospital operations while our investigation continues," he said.
"From tonight, the Tasmanian Health Service is closing the NWRH and the Mersey Community Hospital to visitors, with exceptions only to be granted on compassionate grounds."
Professor Lawler said that in addition to this, from Monday night, Ambulance Tasmania would transport any emergency patients from the Devonport region to Launceston General Hospital, as a temporary measure to reduce the workload on the NWRH while staff were managing the current outbreak.
He said patients, staff and the public will be kept informed of the situation as the investigation progresses.
"It is crucial that the THS does everything it can to support the efforts that are currently being undertaken to trace close contacts of the recently confirmed positive cases, and also to keep patients, staff and the community safe."
Professor Lawler said this change to operations would be constantly monitored and evaluated.
The State's total of coronavirus cases has risen by three in the last day.
Director of Public Health, Dr Mark Veitch, said on Monday night that three new cases had been confirmed since 6pm on Sunday.
This brings the State's tally to 89.
"Two of the cases are women, one is a man. One is from Southern Tasmania, and two are from the North West. Two are aged in their 50s, one is in their 80s," Dr Veitch said.
He said further information on the cases would be released on Tuesday.