Australia were 151-2 in reply to the home side's 197 when heavy showers stopped play 27 minutes before the scheduled lunch interval. Jason Gillespie (28) and Ricky Ponting (19) were the not out batsmen.
Drying up operations were in progress even as dark clouds loomed.
Australia won the first Test in Fatullah by three wickets.
Australia, who had dismissed Bangladesh for just 197 in their first innings, looked set to repair the damage to their reputation after struggling in the opening Test against the emerging side.
They ensured a fine start to their innings with opener Phil Jacques scoring his maiden half-century in only his second Test match.
The left-hander struck 66 with eight fours and one six and was not afraid to play uppish shots in his 98-ball knock.
The 26-year-old looked set for a bigger knock but perished when he tried to sweep a ball from left-arm spinner Mohammad Rafique only to give an easy catch to Shahriar Nafees at mid-wicket.
Australia, expected to whip their lowly opponents, won the first Test in Fatullah by only three wickets.