A total of 11 more Tasmanians now have coronavirus and the state's COVID-19 tally stands at 122.

Coronavirus: All the latest updates on COVID-19 for Tasmania

"Ten of the cases are from the North West. One is from the South," Dr McKeown said.

"Eight of the cases are healthcare workers who have worked at the North West Regional Hospital (NRWH) and or the North West Private Hospital.

"Nine cases are women, two are men."

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Dr McKeown said one of the cases was a teenager, two were in their 20s, three were in their 30s, one was in their 40s, one was in their 60s and three were in their 70s.

"Two cases are patients at the NWRH," he said.

"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.

"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 McKeown said.

"It may 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.

"The situation with coronavirus is changing regularly. People can stay up to date by visiting the Department of Health coronavirus website www.coronavirus.tas.gov.au or the Australian Government Department of Health website at www.health.gov.au."

The release of the latest data came after Premier Peter Gutwein posted an Easter message to Facebook.

"The restrictions we have in place today will not last forever," Mr Gutwein promised.

"We will beat the virus and we will get our old way of life back.

"If everyone abides by the rules, if everyone stays home, that promise of hope for the future which Easter offers will be realised."