Premier Peter Gutwein announced the restrictions would come into force from 6pm on Friday.
People can only leave their homes for five reasons, including shopping for essential supplies and exercise, while a host of businesses will be forced to shut their doors.
"We cannot afford an outbreak and put the safety of Tasmanians, especially vulnerable Tasmanians, at risk," Mr Gutwein said.
It comes after a 31-year-old man, who flew to Hobart via Melbourne on Monday night without a valid border entry pass, tested positive.
He was noticed missing from a Travelodge hotel quarantine facility on Tuesday and was arrested in the afternoon at a home in northern Hobart.
The man, who Mr Gutwein has described as being uncooperative and unwilling to wear a mask, later returned a positive test.
He spent time at two households and Bridgewater Woolworths, which has been declared an exposure site from 3.30pm to 4pm on Tuesday.
Anyone who was at the supermarket between those times has been told to isolate immediately.
The man, who has been fined $3000, was driven away from the Travelodge, by a friend but it remains a mystery as to how he absconded.
Mr Gutwein says extra CCTV cameras have been installed at the hotel and security tightened.
Monday's Jetstar flight JQ715 from Melbourne to Hobart is another exposure site, as are several spots at Hobart Airport that night.
The man was ordered to undergo hotel quarantine as there were no flights available on Monday night to send him back to NSW.
Authorities had identified 38 primary and 16 casual contacts of the man, prior to the Woolworths store being declared an exposure site.
Seven primary contacts have returned negative tests so far and all are in quarantine.
AAP with The Project