State health commander Kathrine Morgan-Wicks detailed the cases during Tuesday's briefing.

A patient in their 60s in a medical ward on the third floor was tested with a rapid antigen test on Monday after displaying COVID symptoms, which came back positive.

Two other patients in the four-bed room were tested, and one returned positive. A fourth patient had already been discharged and is isolating, awaiting the result of a test.

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Both of the positive cases have since been confirmed with PCR tests.

No staff members have been identified as close contacts, given they were all wearing N95 masks and approved eyewear, which had been mandatory since December 31.

A total of five patients were deemed to be close contacts, as the original positive case had been in the Mersey "for some time". All have since been discharged and are isolating. The visitor log is being reviewed for the past 72 hours to determine any other potential contacts.

The hospital has put in place its outbreak management protocol, but Ms Morgan-Wicks said this was a precaution at this stage, and the situation was not yet defined as an "outbreak".

It means all staff in the area are undergoing rapid antigen tests.

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The ward is not accepting new admissions or transfers until the source of the case has been further investigated.

Ms Morgan-Wicks said the two positive cases have been moved to the North-West Regional Hospital which was "in line" with the region's COVID management plan.

The Mersey Community Hospital is at escalation level 2.

Premier Peter Gutwein also outlined changes to Tasmania's border entry requirements, removing the need for testing for vaccinated travellers.

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