The medical ward has been locked down at the Latrobe-based Mersey Community Hospital with no more admissions, visitors or transfers allowed, Tasmania's chief medical officer Tony Lawler said on Wednesday.
One of the newly-infected patients has been transferred to the Northwest Regional Hospital, where two other COVID-19 positive patients were transferred on Monday.
The four other COVID-19 positive patients will remain at the Mersey, where two staff members have also been infected.
However, Prof Lawler said it is still safe to attend Mersey for emergency care, outpatient appointments or procedural treatment.
"The outbreak is currently impacting the medical ward, with other areas of the hospital continuing to operate safely," he told reporters.
"I'm confident that all necessary steps are being taken ... and that at this stage, this is a managed outbreak.
"We hope to transition to a controlled outbreak over the coming days of testing and monitoring. I want to assure you that we have prepared for this."
Twenty-nine people with COVID-19 are in hospital across Tasmania, according to figures released on Wednesday, a rise from 25 reported on Tuesday.
Twelve of them are being treated specifically for virus symptoms, with two people remaining in intensive care.
Seventeen people with the virus are in hospital for unrelated medical conditions.
Tasmania's number of active cases has dropped slightly from Tuesday's figure of 6417 to 6323.
Thirty-six people are staying in community management clinics and 388 are receiving care at home.
Tasmania has dropped border entry testing requirements and travel registration rules for vaccinated arrivals.
Unvaccinated people are still required to return a negative rapid antigen test in the 24 hours before reaching Tasmania and must quarantine for five days on arrival.
16°C