One of the latest cases was hospitalised for unrelated reasons and upon taking a precautionary Covid test, returned positive results.
All other cases are believed to be showing only mild symptoms and are being adequately managed either at home or in a registered quarantine facility.
Premier Peter Gutwein said the lack of serious cases is a testament to the effectiveness of the vaccinations.
"This underlines the fact that vaccination works," he said.
Over 90 percent of eligible Tasmanians are now fully vaccinated with 96 percent on one dose.
Another 10 percent have received their booster jabs.
Despite the rise in cases, Premier Gutwein says there have been no changes to testing requirements for interstate visitors.
"I know it can be difficult, but you need that test if you're coming from a high-risk location," he said.
With the inlfux of visitors for the Christmas holidays, Premier Gutwein said the health department had organised another 100,000 rapid antigen tests for people to do at home.
The premier is urging anyone who returns a positive rapid antigen test to head out and get a PCR test done as soon as possible.
"If you get a positive result, make sure you isolate and organise a PCR test immediately," he said.
"PCR test is the one that's most accurate."
A mask mandate is currently in place for indoor settings except for inside homes.
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