The lockdown will cover the weekend and is due to end on Monday at 6pm.
The lockdown comes after a man from New South Wales absconded from hotel quarantine in Hobart, before testing positive to COVID-19.
The man had travelled to Tasmania via Melbourne despite not having the necessary permissions.
While the man has since been returned to hotel quarantine, Mr Gutwein said he had "not been cooperative".
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.
So far, 39 close contacts have been established.
A primary contact of the man also allegedly breached home quarantine last night.
He was apprehended, fined, and taken to a hotel for isolation.
Mr Gutwein said the lockdown was a result of health advice.
"We simply cannot afford for an outbreak to occur," he said.
"We're at a crucial stage of the vaccination rollout."
From 6pm, Tasmanians in the affected areas will only be allowed to leave home for one of five essential reasons.
People will be allowed to shop for essential supplies and groceries within a 5km radius of their home.
Exercise will also be permitted once a day in the same area.
People can leave homes for essential work or to provide care, or for healthcare reasons.
There will be no indoor or outdoor gatherings, no more than 10 people at a funeral, and no weddings except for compassionate reasons.
Even at a permitted wedding, only five guests will be permitted.
People will not be allowed to visit others' homes unless they are supporting a vulnerable person, as part of a significant relationship, or as part of a singles bubble.
Facemasks will remain mandatory indoors and outdoors, except at home.
Cafes, restaurants and hotels will be open for takeaway only.
However, establishments such as day spas, beauty parlours and hairdressers will be closed.
Supermarkets will be open.
Construction will be shut down for the lockdown.
Bunnings will also be shut, except for tradespeople or those who have an essential need.
Mr Gutwein said support would be available for people whose businesses and employment were affected by the lockdown.
Along with the $1500 disaster payment, Tasmanians can also apply for the pandemic isolation grant.
This amounts to $250 per adult and $125 per child, with a cap of $1000 per household.
Tasmanians who are currently in NSW, the ACT and Victoria will not be permitted to return to southern Tasmania during the lockdown period, Mr Gutwein said.
Returning Tasmanians and other travellers from low-risk locations such as Western Australia, South Australia, Queensland and the NT who are booked to return to Tasmania in the next three days can return home, but must enter lockdown.
"When you arrive, travel to your home without making any unnecessary stops and wear face-masks," Mr Gutwein said.
"You must remain at home during the lockdown period where possible, consistent with the lockdown falls.
"Be prepared to work from home, study from home, and only leave the house when absolutely necessary."