A Tasmanian hospital ward has been closed to visitors and admissions after four patients tested positive to COVID-19.

Other patients in the Launceston General Hospital ward have tested negative on PCR tests, but will be monitored.

Staff who worked in the ward since April 15 have been instructed to take a PCR test.

Tasmania's Acting Health Commander Dale Webster said all of the COVID-positive patients have only minor symptoms and authorities were investigating the cause of the outbreak.

"The public should be reassured it is safe to attend the Launceston General Hospital," he told reporters on Tuesday.

"The outbreak has been confined to the ward and other areas of hospital continue to operate."

It is the fourth COVID-19 outbreak at a Tasmanian hospital since the pandemic started.

There is also an outbreak in the state's prison system, with a total of 104 prisoners and 14 workers testing positive across five sites.

There are 69 active cases left in the outbreak.

"We expect that management will go on for another week or two with further regular sweeps of the prison to identify further cases," Public Health Director Dr Mark Veitch said.

"We hope to see fewer and fewer cases as the next week or so goes on."

There were 1418 new COVID-19 cases and no deaths reported in Tasmania on Tuesday.