Three of the cases had travelled on cruise ships this month.

Director of Public Health Mark Veitch said once again health services were investigating each case to identify and contact close contacts so they could be placed in quarantine.

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

"All the five latest cases have recently returned to Tasmania from overseas," he said.

"They comprise two persons recently returned from the United States, two persons from the Ruby Princess cruise that arrived in Sydney on March 19 and one person from the Ovation of the Seas cruise that arrived in Sydney on March 18."

The number of total cases in the state is made up of 15 cases in the South, two in the North, two in the North West and three cases from interstate travellers.

Dr Veitch said the cases reflected the rapidly increasing incidence of coronavirus infection throughout the world and on cruise ships.

"These cases show why measures to quarantine persons recently arrived from overseas were put in place, followed by measures to quarantine persons arriving from mainland Australia," he said.

IN OTHER NEWS:

"Public Health Services is speaking daily with passengers from the Ruby Princess cruise who are all required to be in quarantine until April 2.

"Passengers on the Ovation of the Seas cruise have already been contacted by NSW Health and advised to quarantine at their final destination.

"Public Health Services will also contact these passengers tomorrow."

Anyone requiring more information about coronavirus should contact the National Coronavirus Health Information Line on 1800 020 080.