Mask wearing will still be mandatory both indoors and outdoors until 6pm on Friday for anyone aged over 12, except for people in their own home or in a vehicle with an immediate family member.
Masks will also not be mandatory for anyone undertaking vigorous exercise.
Residents of the 12 LGAs who travel to another part of the state will still have to wear masks until Friday evening.
Southern Tasmania entered a snap three-day lockdown on Friday after an unauthorised traveller from New South Wales allegedly absconded from hotel quarantine and spent time in the Hobart community before returning a positive COVID-19 result.
Mr Gutwein said the man had “not been cooperative” with health authorities.
He said information had not been disclosed and had been inconsistent, leading to delays in contact tracing.
It’s believed the man spent about 18 hours in the community. A number of primary close contacts were identified.
“We simply cannot afford for an outbreak to occur,” Mr Gutwein said on Friday.
“We’re at a crucial stage of the vaccination rollout.”