Premier Peter Gutwein says the state's health and hospital system is well-placed to manage the coronavirus.
Mr Gutwein said he was absolutely confident the state could handle the response required if cases of the virus were confirmed in Tasmania.
"Our public health system can hope with this particular matter," he said.
But Greens leader Cassy O'Connor said Health Minister Sarah Courtney and Director of Public Health Mark Veitch needed to come out and tell Tasmanians what processes and protocols were in place to deal with the virus.
"My understanding is that in our public hospitals there's a measure of uncertainly among staff about what the processes and protocols are if someone comes in presenting symptoms of the virus," Ms O'Connor said.
"Tasmanians will be hoping that our health system can cope with this new illness."
Labor health spokeswoman Sarah Lovell said she was hopeful the government was keeping an eye on the virus.
"Tasmanians are concerned about the possible impact it may have on many aspects of the Tasmanian community," Ms Lovell said.
Mr Gutwein said the government was viewing the virus seriously and approaching it responsibility and sensibly.
"I've been briefed this morning by the Director of Public health who informs me the whole of government approach we are taking, led by DPAC in concert with health and with other agencies, is the right approach," Mr Gutwein said.
"It is a challenging issue but it is an issue the government has a plan for."
Over the weekend, a man was cleared of the virus at the Royal Hobart Hospital and on Wednesday a woman in her 20s was being tested for coronavirus at the Launceston General Hospital.
In a statement, the government recommended:
- contacts of confirmed novel coronavirus cases must be isolated in their home for 14 days following exposure; and
- people entering Tasmania from Hubei Province of China must be isolated in their home for 14 days after leaving Hubei Province, unless seeking medical care.
"This means that Tasmanian students and staff who have recently been in Hubei Province in China should not attend childcare, schools, or other educational settings until 14 days after leaving Hubei Province," the statement said.
"All Tasmanians, including parents and carers, should be alert for symptoms in people who were recently in China, including fever, cough and breathing difficulties."
For more information, visit www.health.gov.au/health-topics/novel-coronavirus-2019-ncov.