The minister on Sunday said the latest results are encouraging but urged Tasmanians to avoid complacency and stay at home, unless going out for essential reasons.

"We know in other countries we have seen second waves which have had devastating consequences," she said.

"So please I ask all Tasmanians, while this is very encouraging, we cannot be complacent and we must continue to ensure we are complying with all the measures.

"Restrictions remain across Tasmania and police are going to monitor those."

Twelve of Tasmania's 13 COVID-19 deaths have been in the northwest, and two-thirds of an overall 221 cases have come from the outbreak in the region.

But Premier Peter Gutwein said on Saturday that with the northwest outbreak under control, the tighter restrictions there would be eased from Monday.

Ms Courtney said that doesn't mean restrictions in place across the state should be overlooked.

"Now is not the time to go out and do a bit of retail shopping to just to buy a pair of shoes because you feel like it. These shops are open for essential reasons," she said.

"You cannot go over to a mate's place for a barbecue."

The North West Regional Hospital at Burnie is also set to be gradually reopened.

The resumption of maternity, radiation, oncology and intensive care services will be prioritised this week, Ms Courtney confirmed.

The Spencer Clinic, a mental health inpatient unit, will also be up and running again during the week.

In the south, the Royal Hobart Hospital's new hyperbaric oxygen therapy chamber will be open from Monday, meaning it could potentially support COVID-19 patients who can't get oxygen through a mask or a hood.

The chamber will also be able to treat people with injuries from radiation, diabetic wounds and those with serious infections such as gangrene.

Overall, Ms Courtney said as of Sunday there had been 221 confirmed cases of COVID-19 and 158 of those people had recovered.

Australian Associated Press