The childcare centre subsidy adds to a growing list of support packages worth some A$200 billion (US$121 billion) for airlines to mall owners as the government attempts to "hibernate" the Australian economy, to be reawakened when the crisis has passed.
"We will demonstrate to the world here in Australia how such societies can deal with these sort of challenges our way, the Australian way," Morrison said during a televised press conference. "So stay positive, Australia. Stay connected, stay strong. We will get through this together."
Morrison and state officials have introduced unprecedented restrictions on public movement to stop the spread of the virus and said that data on new infections continued to show those efforts were paying off.
"The curve is beginning to flatten," Health Minister Greg Hunt said. "It isn't sustained yet, it hasn't been consolidated, but those early, important signs are absolutely critical."
Morrison said on Thursday the country's testing rate was now more than 1,000 tests per 100,000 people, or 1 per cent of the population.
"We are the first country to the best of our knowledge that has been able to exceed that mark," Morrison said.
Childcare centres have lost significant business in recent weeks as thousands of people shifted to working at home, or were made redundant.
Morrison said the subsidy would keep about 13,000 childcare centres open by paying them A$1.6 billion over the next three months. The full subsidies will last for six months, when they will be reviewed.
Keeping the centres open would also allow critical workers from medical professionals to cleaners and food deliverers to continue to work, Morrison said.
Australia has ordered the shutdown of restaurants, cafes, bars, movie theatres and instructed people to stay inside unless they are shopping for food or taking their daily exercise as it tries to contain the flu-like illness.
The restrictions are expected to push the country's A$2 trillion economy into its first recession in almost three decades and lift unemployment to double figures.