Travellers who have arrived in Tasmania from Western Australia since January 26 are being urged to check the list of risk locations, which includes 17 sites across Perth.
The list is available here.
A hotel quarantine worker in Perth visited the locations while infectious between January 25 and 30.
Premier Peter Gutwein said anyone who visited the sites at the specified times must self-isolate and call the Public Health Hotline on 1800 671 738.
He said the situation showed how vigilant Tasmania must be in regards to stopping the spread of COVID-19.
"It's important that Tasmanians remain vigilant, that they don't become complacent," Mr Gutwein said.
IN OTHER NEWS:
"If you're unwell, don't got to a function, don't go to a party and importantly don't go to work."
A flight from Perth will arrive in Tasmania this afternoon, but acting director of Public Health Scott McKeown said those who are allowed to enter the state will have been approved under the G2G system.
"Anyone though who has recently travelled from WA, regardless of whether attended one of the locations or not, should monitor the list regularly as it will change as the public health response changes," he said.
"If a person hasnt attended any of those locations, they pose a low risk but we're asking them to continue monitoring the list if it changes, and continue to monitor their health."
Advice remains the same for anyone who visited high risk locations in New Zealand, available here.
New Zealand travel bubble plans continue to progress
Mr Gutwein said he expected flights between New Zealand and Hobart could begin by mid-March.
Works have been progressing at Hobart Airport to implement the required biosecurity measures.
Mr Gutwein said that, despite the recent outbreak in New Zealand, the fact Tasmania was open to the Eastern Seaboard, South Australia and Northern Territory after their outbreaks showed that those challenges could be overcome.
"[Of our nearby international neighbours], the one that we have the strongest and most likely chance of having a travel bubble operating appropriately would be New Zealand," he said.
Vaccine preparations continuing
Three hubs for the distribution of the Pfizer vaccine will be established in Tasmania: at the Royal Hobart Hospital, Launceston General Hospital and North West Regional Hospital.
The government expects these to become available for high risk people near the end of February.
The hubs will only deal with the Pfizer vaccine.
Separate plans will be developed for the AstrtaZeneca vaccine for the wider population.
Prime Minister Scott Morrison is expected to give a further update later on Monday.