Thirteen of the 36 positive coronavirus cases in Tasmania are linked to cruise ship the Ruby Princess.
Public Health director Mark Veitch on Wednesday morning said of the eight new cases diagnosed on Tuesday, four were linked to the ship.
He said two of the new cases had arrived from different parts of the United States, one case from the Ovation of the Seas cruise ship and another from the Carnival Spirit.
That cruise ship had arrived in Melbourne on March 14.
"That is not a vessel we were previously aware of having coronavirus infection on it," Dr Veitch said.
He said the vessel left Melbourne on March 2 and stopped at various ports in New Zealand.
Dr Veitch said any Tasmanian who had been on that trip and had been unwell since should contact the Public Health Hotline urgently.
Nineteen Tasmanian cases have been associated directly or indirectly with international travel and seventeen with cruise ships.
Dr Veitch said four cases had been cleared of infection.
There has been no evidence of community transmission yet.
Premier Peter Gutwein said there would be stricter border restrictions imposed from today, more aggressive contact and tracking, and a hardline approach to self-isolation and management of positive cases.
"I expect community transmission will happen at some stage and these measures will give us a fighting chance to control it," he said.
"I will not hesitate to take further measures, and if necessary, shut the state down to only running essential services."
Mr Gutwein said all non-essential travellers to the state without a residence in Tasmania would be instructed to either return to their departure point or would be directed to accommodation provided by the government for 14 days of self-isolation at a cost.
He said basic supplies would be provided to them at the airport or ferry terminal.
"Whilst in self-isolation, they will be monitored and provided with support," Mr Gutwein said.
"If they break the rules, they will be charged with an offence."
He said if a Tasmanian resident who had returned home was required to self-isolate for 14 days, all members of the household had to do so as well and not leave the property.
Mr Gutwein said if this could not occur due to somebody having an essential occupation, the government would provide accommodation at no cost.
He said Tasmanians should not travel to King and Flinders islands for a holiday as they would be required to self-isolate for 14 days.