The woman, from the state’s north-west, was being treated at the Launceston General Hospital before she passed away.
Meanwhile, the state recorded no new cases of the virus overnight.
Premier Peter Gutwein said that news, combined with the death of another Tasmanian, was conflicting.
“As I’ve continually said, there will be bad days,” he said.
“But there will also be better days as well.
“Today unfortunately is another one of those bitter sweet moments.
“To stand here and have to announce that we’ve lost another life is something that gives me deep concern and is something that I must admit troubles me deeply.
“However, what it does do, it sharpens my resolve to get on top of this and stamp out this insidous virus.”
Gutwein urged Tasmanians to be cautious, and extended the state’s ban on non-essential retailers until May 3.
The restrictions had been due to be lifted this weekend, but Gutwein said there needs to be more testing done before the state can risk it.
“It’s not a decision that is taken lightly,” he said.
“I know many in the north-west will be unhappy about this.
“But we need to get on top of this. We need to stamp this out. We need to crush this virus.”
Tasmania has recorded 205 cases of coronavirus, including nine deaths and 106 cases which have since fully recovered.
