Health authorities have urged Tasmanians to get their flu vaccination as soon as possible to avoid people becoming ill with both the flu and COVID-19 at the same time.

Coronavirus: All the latest updates on COVID-19 for Tasmania

Ms Courtney said the government was working to get supplies of the flu vaccine from the National Immunisation Program.

"We are engaged with both the suppliers and logistics [staff] to make sure they are getting into the state," Ms Courtney said.

"There have been some challenges about that but we are working on that."

Ms Courtney said the ordering system for GPs to secure vaccination stocks opened on Wednesday night.

"They will distributed very soon," she said.

"We are making sure that as we do this we prioritise those most vulnerable groups, so that will be aged care and people that work in health care settings."

But Labor health spokeswoman Sarah Lovell said Tasmania needed to set out a plan to ensure the COVID-19 crisis was not worsened by the upcoming flu season.

She said steps taken by the Federal government would only deliver enough flu vaccines for half of Australia's population.

"Doctors will have to prioritise those most at risk, including the elderly, vulnerable Tasmanians and health care workers," Ms Lovell said.

"That leaves a large proportion of Tasmania's population unprotected from flu at the same time we are seeing the start of community transmission of COVID-19.

"We can't assume that social distancing will be enough to protect us."