It marks the eighth consecutive month that the rate has fallen and the lowest unemployment figure since December 2010 despite that Melbourne, the capital city of Victoria state, spent early June in a coronavirus lockdown, reports Xinhua news agency.
Treasurer Josh Frydenberg said the data was a testament to the "resilience" of the Australian economy.
"It doesn't, however, take into account the New South Wales (NSW) lockdown -- a reminder of the challenging days ahead," he said.
NSW on Wednesday announced to extend the lockdown on the Greater Sydney and surrounding areas for at least another two weeks.
The number of unemployed Australians actively looking to work fell to about 679,000 in June compared to a peak of 1 million in July 2020.
Youth unemployment dropped half a percentage point to 10.2 per cent, which was 1.4 percentage points below the rate at the start of the pandemic.
However, the total number of hours worked by Australians fell 1.8 per cent in June from May.
"Hours worked data continues to provide the best indicator of the extent of labour market impacts from lockdowns," Bjorn Jarvis, head of labour statistics at the ABS, said in a statement.
"Hours worked in Victoria fell by 8.4 per cent in June, compared with a 0.3 per cent fall in employment. This highlights the extent to which people in Victoria had reduced hours or no work through the lockdown, without necessarily losing their jobs."