Gutwein said the man was not given a clearance to travel to Tasmania from NSW.
"He arrived without having an endorsed pass," he said.
The man flew into Launceston on August 2 and was tested while in hotel quarantine before returning to NSW on August 4.
His positive result did not come through until Wednesday morning after he had already left.
The man did not spend any time in the Tasmanian community.
"Again, I do want to make the point that this is not a case of community transmission," Gutwein said.
"Now contact tracers have immediately started tracking and tracing."
The Premier said it was unclear if the man had broken lockdown measures or Covid protocols in NSW but it was likely he had.
Tasmania Health Minister Jeremy Rockliff said he wasn't aware that the man had breached any public health directions in Tasmania.
"Obviously, if he did, we'd look at that," he said.
"But I think this is an example not so much of someone breaching a public health direction but (of) processes.
"I sincerely hope mitigating the risk and enabling us to get on and manage any residual risk with contact tracing and follow up."
Gutwein urged people not to panic and said there was no need for stricter restrictions or a lockdown at this stage.
"Firstly, we're not going to be asking anyone in northern Tasmania to close their business or lock down at this stage," he said.
"As I've said, it's an occasion in quarantine with a well-understood travel corridor."
Meanwhile, Tasmanian authorities have also decided to pull out of hosting its scheduled AFL game between Collingwood and Hawthorn.
The game was set to be played this weekend at the University of Tasmania Stadium in Launceston but has been canned over fresh Covid fears.
The match was to take place on Sunday at 2.10pm local time.
Gutwein said he had reached out to the AFL but had not yet spoken with the league's chief executive Gillon McLachlan about the decision.
- NCA NewsWire
