Steve Smith's side was chasing 183 to beat Bangladesh at The Oval when persistent drizzle forced the players from the field.
Having scored 83-1 from 16 overs, Australia only needed to play for four more overs to be eligible to win via the Duckworth-Lewis rule for rain-affected games.
Instead, Smith and his team-mates were reduced to anxiously looking at weather updates and peering upwards for any sign of a break in the slate grey sky.
Australia will be cursing their luck as they were also frustrated by bad weather when their opening group fixture against New Zealand was abandoned, although on that occasion they were in a less commanding position.
With England, who won their opener against Bangladesh, due to play New Zealand in the next Group A fixture, two-time champions Australia will have to beat the hosts in Birmingham on June 10 to qualify for the semi-finals.
Tamim Iqbal's 95 was the highlight for Bangladesh, who are winless and face New Zealand in their final group tie.
Aware that ominous clouds were gusting in, Australia needed to get off to a fast start to have a chance of winning on the D/L rule if the required 20 overs were bowled.
Aaron Finch and David Warner both crushed a pair of fours as Australia raced to 37-0 in six overs.
Warner was especially aggressive, pulling one tame delivery from Mashrafe Mortaza off his hip and away to the fence in a flash.
Rubel Hossain briefly stemmed the tide when the Bangladesh seamer dismissed Finch lbw with an inswinger the opener couldn't handle as he played across his pads.
When Warner's total reached 37 he had passed 4,000 runs in one-day internationals.
Only South Africa's Hashim Amla and West Indies legend Viv Richards hit that milestone quicker than Warner's 93 innings.