Additional restrictions were placed on the region due to a coronavirus cluster among health workers, which was traced to the ill-fated Ruby Princess cruise ship.
All businesses were closed except for medical services, while the North West Private Hospital was also ordered closed.
Gutwein said the local, additional restrictions will be lifted, but the state will continue to have its existing restrictions.
“We are confident that those additional restrictions, placed on the north-west on Sunday almost three weeks ago, on April 12, will be able to be lifted,” he said.
“Meaning on Monday, May 4, the businesses and services which were impacted by those additional restrictions can re-open, and the workers and staff will be able to return to work.
“It’s important to note this will only be the lifting of the additional restrictions.
“The statewide restrictions in place in terms of personal movement, the operation of certain businesses, will still apply.”
Of Tasmania’s 221 confirmed coronavirus cases, 147 are in the north-west, including 12 of the 13 deaths.