Passengers on a cruise ship in Hobart are being held onboard and tested for COVID-19 after two confirmed cases.

Public health officials are also concerned about a rising number of infections associated with a music festival at Launceston with 25 linked to the event so far.

Tasmania's Premier Peter Gutwein said the two people who tested positive on the Coral Discoverer have been removed from the vessel.

About 60 passengers and 30 staff remain on board and are being tested for the virus with contact tracing to continue over the next two days.

The ship's operators have activated their COVID response plan to manage the outbreak and ensure no broader risk to the wider community.

"We will continue to work closely with the vessel to ensure that any risk on board is being managed and to ensure there is no broader risk arising from the two cases that have occurred," Deputy Director of Public Health Scott McKeown said.

The premier said the people who attended the Party In the Apocalypse at Launceston's Inveresk Park on December 27 and 28 were also being asked to carefully monitor for symptoms with two dozen infections now linked to the event, attended by about 10,000 fans.

"I want to be really clear (that) this does not mean that everybody who attended Party in the Apocalypse needs to turn up at a testing clinic or take a rapid antigen test," he said on Monday.

"But if you were at that event, you need to use your commonsense and monitor for symptoms and if symptomatic please call the public health hotline and go and get a PCR test."

The two areas of concern come as Tasmania reported a record 466 new COVID-19 cases, although Mr Gutwein said the majority were experiencing only mild symptoms.

Only two people with the virus are in hospital and both were admitted for other reasons.

Active infections have climbed to 1691 cases, but the premier said about 50 per cent of people were choosing not to use the COVID at home service because they were not symptomatic or were not feeling particularly unwell.

"Importantly, what we're seeing at a national level is whilst case numbers are increasing as a result of the transmissibility of this disease, hospital numbers and ICU presentations are but a fraction of those overall cases," Mr Gutwein said.

"I can understand people being a little anxious, it's important people do stay calm.

"We need to ensure we step through this carefully, sensibly and responsibly as we manage the transition program that we have underway at the moment."

But the Labor opposition said the government's reopening plan had created such uncertainty and anxiety in the community that much of the economy, businesses and workers were not benefitting at all.

"Alongside family reunions, the economy, including hospitality and tourism, were key reasons behind the border reopening, however, the government's failed plan is putting increased pressure on them," Workplace Relations Spokeswoman Sarah Lovell said.

"Changes to close contact rules and the notification of exposure sites, a lack of transparency and communication from the government and surging case numbers have seen many businesses struggle and some even make the decision to temporarily close to ensure the safety of staff and the community."