This comes days after it was confirmed a 20-year-old man who tested positive to the virus has attended work in the city and two popular waterfront nightspots when health officials had told him to remain in isolation to await test results.

The new clinic is in addition to a similar one set up in Launceston last week.

Health Minister Sarah Courtney said the clinic at the Statton Building of the Repatriation Hospital would be operated by nurses during normal business hours.

She said people needed to first call the Public Health Hotline on 1800 671 738, or visit their general practitioner, before they accessed the clinic.

"After being referred to the clinic, patients will be assessed and tested by a nurse and asked to return home to self-isolate until they have been told their test result," Ms Courtney said

"Results will usually be available within 24 hours."

She welcomed the federal government's announcement on Tuesday that an additional 54 million face masks would be delivered to frontline professionals managing the response to the virus.

"The supply issues for masks are a global challenge, and I encourage Tasmanians to heed public health advice that the use of face masks by the general public is not recommended," Ms Courtney said.

"This helps to ensure availability when they are clinically needed, such as in dental practices, the medical sector and for those in contact with a suspected case."

Labor on Tuesday accused the state government of not doing enough to resist the spread of coronavirus in Tasmania.

Labor health spokeswoman Sarah Lovell said people were understandably concerned with the Hobart man's failure to comply with isolation requirements but added Premier Peter Gutwein's threats of fines for further non-compliances were counterproductive.

"Obviously, we want people to comply with self-isolation directives, but instead of bullying people by threatening fines they can't afford, we need to understand why people may not be self-isolating when advised to do so," she said.

"Many Tasmanians are under-employed, casual, or may not have reserves of personal leave, and can't simply take time off work, without facing significant financial hardship.

"Threatening people with fines may only deter them from being tested in the first place, leading to a much higher infection rate."

Premier Peter Gutwein said this was not a time for politicking from the Labor Party.

"In an astonishing move the Labor party is making itself the expert on public health," he said.

"We have, and will, continue to take our advice from our public health experts, both at a state and national level, and continue to work with the federal government to ensure people who are in self-isolation have the supplies and support they need."