Tasmania has ordered recent arrivals from Victoria to wear a mask in public settings and avoid crowds.
The directive covers people who have been in Victoria since July 8 and comes into force from midnight on Friday.
Tasmanian Premier Peter Gutwein said the order was made out of an "abundance of caution".
"What we're seeing in Victoria at the moment is a very rapid escalation in the number of exposure sites," he told reporters.
Tasmania had already put up a hard border with Victoria from midnight on Thursday, which means only essential travellers are allowed to enter.
Mr Gutwein said about 15,000 people had arrived in Tasmania from Victoria since July 8.
Victoria recorded 10 new COVID-19 cases on Friday, the first day of a statewide five-day lockdown, taking the outbreak to 24 cases.
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