A respiratory clinic for coronavirus testing will be opened in the North-West in the near future.
Two clinics are already operational in Launceston and Hobart.
Health Minister Sarah Courtney said the government was in the final planning stages of further clinics.
Ms Courtney indicated she would have more to say about a clinic in the state's North-West on Thursday.
"We want to ensure that we've got good spread across the geography of Tasmania," Ms Courtney said.
"[For] Tasmanians that are in more remote and regional facilities, we want to ensure that testing can be delivered should that be required by Public Health."
A third case of coronavirus in Tasmania was confirmed late on Wednesday evening.
Ms Courtney said the risk to Tasmanians from casual contact with a confirmed case was low.
"National health advice remains that the risk to the general Australian population is low, with the majority of cases being from returned travellers," she said.