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.
Get the latest breaking news from SCA newsrooms around Australia. Short, simple and everything you need to know.
