The entire mainland will be designated as high-risk from 4pm today, after SA recorded five new cases.
SA will begin a seven-day lockdown from 6pm Tuesday.
Gutwein said anyone who returned since July 8 is required to wear a face mask for 14 days after arrival into Tasmania.
Victoria and New South Wales are the other two states to remain high-risk.
People aged 12 years and older are required to wear a mask in public.
"Our priority here continues to be on protecting the health and safety of Tasmanians," Mr Gutwein said.
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