The 37-year-old man, who arrived on a flight from Sydney on Wednesday, was discovered missing from his room at Peppers Seaport in Launceston around 9am on Thursday.

He was arrested in the nearby suburb of Newnham about an hour later and has been charged with failing to comply with emergency directions.

Tasmania's Director of Public Health Dr Mark Veitch has since confirmed the man tested negative for COVID-19

"He posed no infectious risk to the community," he said in a statement.

Earlier, Premier Peter Gutwein said the investigations suggested the alleged escapee had "minimal contact" with people despite spending about nine hours in the community.

In mid-October, a coronavirus-infected NSW man left hotel quarantine in Hobart, sparking a three-day lockdown across the south.

Despite spending time at several houses, a park and a Woolworths supermarket, he didn't spread the virus.

The incident forced a state government review of quarantine facilities and the tightening of security measures.

Mr Gutwein said security and police were in attendance at Peppers Seaport.

"We're doing everything we can but we're not running a prison system. We don't put barbed wire around these hotels. We simply expect people to abide by the law," he told reporters.

The man apparently climbed over a third-storey balcony and went down the side of the hotel, Mr Gutwein said.

Police say the man didn't have approval from the deputy state controller to enter Tasmania and was subsequently told to quarantine.

Tasmania is closed to NSW but will open its borders to all fully vaccinated travellers on December 15.

Australian Associated Press