The two-day match at Fatullah, slated to start Tuesday, had been in doubt since heavy rain partially flooded part of the field.
It was the only warm-up fixture of the tour, Australia's first to Bangladesh in more than a decade.
The Bangladesh Cricket Board (BCB) offered alternative venues but the Australians were reluctant to change at the last minute due to security concerns.
"The BCB has been fantastic trying to get us the game. The amount of rain hasn't helped," coach Darren Lehman told reporters in Dhaka.
Bangladesh's disaster agency says 115 people have died since heavy monsoon downpours hit the region last week, flooding one-third of the country.
Australia have not toured Bangladesh since 2006, and the Test starting next Sunday at Dhaka's Sher-e Bangla National Stadium has been long in the making.
They were due to play two Tests in Bangladesh in October 2015 but the tour was cancelled over security fears after attacks by Islamist extremists in the Muslim-majority nation.
The Australians will play two Tests before departing Bangladesh on September 9.
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