The potential measures come after large crowds gathered on Sydney's beaches including Bondi on Saturday, flouting social distancing advice.
Mr Morrison said the situation at Bondi Beach should be a "wake up call to take these policies seriously".
He also announced a financial package to assist the country's economy during the crisis.
The number of coronavirus cases in Australia has topped 1,000 and seven people have died.
Bondi Beach was temporarily closed on Saturday after crowds exceeded Australia's 500-person outdoor gathering limit. It remains closed on Sunday.
Mr Morrison mentioned the incident and appealed for Australians to show common sense when it comes to following the rules.
"You have to keep a healthy distance between each other," he said.
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