The snap three-day lockdown for 12 municipalities was announced by Premier Peter Gutwein at 2.30pm on Friday after an "increasing number" of contacts connected to a COVID-positive case were identified.

During a COVID-19 update on Saturday morning, Mr Gutwein said the government had acted swiftly and the steps being undertaken were important.

"I am very pleased to say this morning we have no further positive cases at this time," he said.

"We now have 158 primary close contacts which we are working with."

Public Health director Dr Mark Veitch said there had been a big jump in the numbers of primary contacts compared to Friday's numbers.

He said more testing and working through referrals would be undertaken over the next few days.

Nineteen casual contacts related to the positive COVID-19 case were identified previously.

Dr Veitch said no further exposure sites had been declared.

Mr Gutwein said in the past 24 hours there had been 1402 COVID-19 tests collected.

Tasmanians have achieved an 83 per cent vaccination rate for first dose, with 68 per cent fully vaccinated.

"Our aim is not to prolong [the lockdown] ... short and sharp as possible," Mr Gutwein said.

"It's taken one individual to do the wrong thing and leave the heavy lifting to everyone else."

Mr Gutwein reiterated there was financial support available for those affected by the lockdown, with more information on the coronavirus website.

The lockdown is expected to be in place until Monday at 6pm when it will be reevaluated.

The lockdown came after the escape of the COVID-positive traveller from quarantine in Hobart earlier this week.