A healthcare worker employed at a Tasmanian hospital is among 11 new cases of coronavirus confirmed today, bringing the state tally to 58.

The worker was employed at Mersey Community Hospital at Latrobe, in the state's north.

In a statement, acting director of public health at Public Health Services (PHS) Dr Scott McKeown said an investigation had begun to determine the worker's movements and identify anyone who they had been in close contact with the worker at the hospital or in the community.

"Should any close contacts be determined through this investigation, these people will be contacted by PHS," Dr McKeown said in the statement.

How the person caught the virus was also being investigated.

Dr McKeown said the worker was fully cooperating with PHS staff.

Of the other cases in Tasmania, eight are related to people who have been aboard cruise ships.

Two other cases are people who have recently travelled to Tasmania from overseas.

Five of the state's coronavirus cases are from northern Tasmania, four are from southern Tasmania and two are from the North-West.

Seven of the cases are men; four are women.

Tasmania has conducted 1,779 tests for coronavirus.