Of the fresh cases reported on Wednesday, 333 are being managed at home and 72 at a community facility.

The active cases have come from 2412 tests.

Five people with coronavirus are in hospital for unrelated medical conditions.

Tasmania's previous daily high was 702 cases reported on Tuesday.

It comes as the state government launches a testing blitz on remote King Island due to concerns a positive case visited several large events before knowing they were infectious.

The state's health department has urged anyone on the island with symptoms, regardless of how severe, to isolate and get tested as soon as possible.

King Island, which sits in Bass Strait off Tasmania's northwest coast, has a population of about 1700 people.

A testing team will arrive on Wednesday to help conduct PCR tests.

"There is concern that a case attended several large private and community events late last week and over the weekend before they knew they were infectious," State Public Health Director Mark Veitch said.

"Testing has been occurring over the past few days, but this is being increased to ensure that anyone on King Island who needs a test can get one as quickly as possible.

"If you have symptoms, do not go to work or visit other people."

The positive case on King Island was confirmed several days ago.

Meanwhile, sixty passengers and 30 crew aboard the Coral Discoverer cruise ship berthed in Hobart have been ordered into seven-day quarantine.

They were deemed close contacts of two COVID-positive people who were removed from the vessel on Monday.

Forty staff from the Royal Hobart Hospital have been furloughed, with Health Minister Jeremy Rockliff declaring Tasmania can expect to hit 2000 daily cases within weeks.

The state had no cases when it opened to mainland high-risk areas on December 15.

Australian Associated Press