Marcia, a category five storm, had weakened after slamming into the Queensland coast late Thursday causing widespread devastation, but its residual effect caused persistent rain over Brisbane.
The match has been in serious doubt for the past few days but the organisers had hoped that curtailed game could be played. The scheduled 03:30 GMT (2:30pm local time) start was delayed and toss between the two captains did not happen. After rain persisted, the match was called off around 4:45pm local time (12.15pm IST).
Australia and Bangladesh are now at the second and third spot respectively in Pool A standings. New Zealand, with two wins from two matches, are on top.
It was the first wash out of the ongoing World Cup. Only one World Cup contest has ever been washed out without a ball bowled and that was back in 1979 in the game between Sri Lanka and West Indies at The Oval.
Australia captain Michael Clarke had been set to play today after missing the co-hosts' opening 111-run win over England in Melbourne last weekend as he continued to recover from his long-standing hamstring injury.