The two hospitals were closed on April 13 to undergo a deep-clean following an outbreak of COVID-19 at the NWRH which saw all staff at both facilities quarantined for two weeks.

COVID-19: The latest updates for Tasmania

It was initially announced by the government the hospitals would be reopened after 14 days.

The emergency department at the NWRH reopened on Friday, staffed by Australian Defence Force and Australian Medical Assistance Team members.

Health Minister Sarah Courtney said she was expecting services at the hospitals to be recommencing within weeks.

"And we will look at the clinical requirements and clinical need around that," Ms Courtney said.

Ms Courtney said high-priory areas of the ED, maternity and pathology would be cleaned first and reopened with the rest of the hospitals to follow in a staged way.

She said a signification amount of work was being done with staff coming out of quarantine to ensure they felt confident about returning to their workplaces.

Ms Courtney said she hoped maternity services would recommence as soon as possible.

"The decluttering and cleaning process does take a period of time and we don't want to rush something that needs to be done in such a meticulous way for the safety of our staff and patients," she said.

"The full provision of the suite of maternity services will take some days to come on board as we finish that clean and ensure that the supporting infrastructure at the site is there to support the mums and babies."

Meanwhile, a mobile COVID-19 testing clinic will be deployed to Smithton on Wednesday.

"That will be able to provide testing for that community then I expect later in the week that will be deployed to the West Coast," Ms Courtney said.

"If you don't have a mobile clinic available in your community, you can still be tested by your GP."