Tasmania hopes to vaccinate all priority groups against coronavirus by early April as part of a national rollout.
Premier Peter Gutwein has announced 2340 doses of the Pfizer vaccine will arrive each week from late February, with that amount to double by late March.
Quarantine and border workers, aged care and disability staff and residents and health care workers are among the priority groups.
"I am pleased to announce the rollout of this vaccine will begin in Tasmania later this month," Mr Gutwein said on Friday.
"We plan to fully vaccinate Tasmania's priority populations by early April.
"(But) the vaccination is not a silver bullet and it's critical we continue to be COVID safe."
The island state will lift capacity restrictions on indoor seated venues, such as cinemas and theatres, to 75 per cent.
If there is more than one person per two square metres, patrons and staff will need to wear masks.
Tasmania has banned travel from three regions in Western Australia - Perth, Peel and the South West - but an easing of restrictions for the latter area is expected before the weekend.
Fourteen premises in Victoria and nine in New Zealand remain classified as high risk.
Four people in Tasmania who visited high-risk premises in Victoria have tested negative but remain in quarantine, Mr Gutwein said.
Apart from the WA and Victoria restrictions, Tasmania is open to the rest of the country.