Masks will be required to be worn by people in non-residential indoor settings or on public transport from Tuesday.

"Public Health has been actively considering whether to include a mandate for mask wearing to further reduce the spread of COVID 19," Mr Gutwein said on Sunday.

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"We think it's important that we take these extra steps to ensure that we keep our community safe."

The mandate will come into effect at 12.01am on Tuesday, December 21.

Masks will be mandatory in all indoor settings, including offices, supermarkets and restaurants.

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Mr Gutwein said masks would also be mandatory at the gym, unless undertaking "vigorous activity".

"Just use your common sense," he said.

"Masks will be mandatory for all indoor settings, so that will include offices, restaurants, pubs, clubs, also including public transport, or in taxis or ride sharing retail setting supermarkets."

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Despite it not yet being mandated, Mr Gutwein strongly recommended people start wearing masks indoors from today.

Public Health Director Mark Veitch said the first three cases of COVID detected in Tasmania since borders have reopened are the Omicron variant, with results for the four other cases yet to be determined.

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