ABS head of labour statistics Bjorn Jarvis said this was the lowest rate since 1974 - when the survey was quarterly.
"The large fall in the unemployment rate this month reflects more people than usual entering employment and also lower than usual numbers of employed people becoming unemployed. Together these flows reflect an increasingly tight labour market, with high demand for engaging and retaining workers, as well as ongoing labour shortages," Mr Jarvis said.
Employment increased by 88,000 and unemployment fell by 54,000.
This means there is now roughly one unemployed person per job vacancy, according to the Bureau - 494,000 to 480,000 respectively.
This contrasts with the pre-pandemic ratio of 3.1 times the number of unemployed people as there were job vacancies.
The underemployment rate however increased by 0.3 percentage points to 6.1%, making the underutilisation rate 9.6% - equal with May's data.
According to ANZ bank economists, this places increased pressure on the Reserve Bank to hike the cash rate in August and beyond.
"We currently expect a third consecutive 50 basis point hike from the RBA in August, with three 25 basis point hikes to follow by early-2023," they said.
"The global experience, inflation momentum and tightening labour market are making it more difficult for the RBA to shift down from 50 to 25 basis point moves.
"The population increase in quarter-two was almost double that of the same time last year, but while new arrivals add to the supply of workers, they also add to the demand side.
"As we noted earlier this year, an unemployment rate in the 2s is not out of the question."
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Special offer: Savings Accelerator (Kick Starter offer).
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Harry O'Sullivan
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