An an annual basis, prices have fallen by 0.3 per cent - a level significantly below the Reserve Bank of Australia's two to three per cent target for any given year.
"Thereafter it is likely rental rates will fall further and will take quite some time to recover to previous highs".
There was a 95 per cent reduction in childcare costs over the June quarter, along with a 16.2 per cent drop in preschool and primary school fees.
"Excluding these three components, the CPI would have risen 0.1% in the June quarter", the ABS chief economist, Bruce Hockman, said.
The data was largely in line with economists' expectations for inflation to drop by around 2.0 per cent but still struck them as remarkable.
"An historic day", said CommSec chief economist Craig James.
"Fortunately policymakers today have responded differently to back then, applying significant fiscal and monetary stimulus to limit the length and severity of the downturn".
But tobacco, alcohol, packet food and furniture prices all increased in the three months to June 30.
The Bureau picked out cleaning and maintenance products (+6.2%); other non-durable household products, which includes toilet paper (+4.5%); furniture (+3.8%); major household appliances (+3.0%); and audio, visual and computing equipment (+1.8%).
While fuel and childcare costs were down, rent also decreased slightly over the quarter, falling 1.3 per cent.
"This time around, although we are in recession now, the fall in the CPI is more the result of the one-off fall in childcare prices due to the Government's decision to make it free for part of the shutdown and the fall in petrol prices".
By 1323 AEST, the Australian dollar was buying 71.70 United States cents after initially dropping to as low as 71.49 U.S. cents following the inflation announcement.