Dr Veitch said four more people were diagnosed with COVID-19 in Tasmania since 6pm Wednesday.

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"This brings the state's tally to 111," he said.

"All four cases are from the North West. One of the cases is a close contact of a previously identified case."

Dr Veitch said three cases were healthcare workers from either the North West Regional Hospital or the North West Private Hospital. He did not specify how many cases were from each hospital.

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"The Outbreak Management Team is already identifying and contacting any person who has had close contact with any of these staff and will ensure necessary actions are taken," Dr Veitch said.

"In addition, Public Health Services is also following up household and social contacts of all confirmed cases.

"If any hospital staff member or patient is determined to be a close contact of these cases, they will be contacted and advised of the action they need to take."

Dr Veitch said it could be necessary for other staff and patients to be tested for coronavirus as investigations progress.

"We will assess and test any symptomatic staff member or patient who is symptomatic and has been at risk of exposure to coronavirus," he said.