Employment, however, fell by 3900 jobs to 12.575 million in the month and the participation rate fell by 0.1 point to 65.5 per cent.
The dip in the unemployment rate has defied the expectations of economists, who had tipped it would stay at 5.4 per cent with a 15,000 increase in jobs in the month.
The rate has remained between 5.4 and 5.6 per cent since mid-2017.
Mr Morrison says the figures are vindication for the government's economic agenda.
He stresses the jobless rate has reached its lowest point since November 2012, while for young people it is at its lowest level since March of that year at 11.1 per cent.
"This government is a jobs machine, working together with the Australian economy that is a jobs machine, that is responding to the economic policies," he told parliament.
Deputy Labor leader Tanya Plibersek said the "very small drop" in the unemployment rate was welcome.
But she said the opposition is worried the latest figures show a rise in the number of people out of the job-seeking market.
"We are concerned about the continuing rates of underemployment and of people who are giving up looking for work," she said.
"We need to see a system that sees stronger employment growth and better-paying conditions."