He was India captain Rohit Sharma's opening partner in the home T20 series against Afghanistan earlier this year but his place looked under threat as he struggled for runs in the IPL
The tourists had been scheduled to play a two-day practice match against a Bangladesh Cricket Board XI from Tuesday before the first Test in Dhaka begins on Aug. 27.
"We've decided to not do the tour game now which is a shame for both sides, the Bangladesh Cricket Board (BCB) has been fantastic trying to get a game," Australia head coach Darren Lehmann told reporters on Monday.
"The amount of rain they've had can't be helped... It's a shame we're not playing but we've got great facilities here."
The BCB had reportedly proposed alternative venues but Australian team management rejected them for logistical reasons.