The umpires abandoned play soon after the scheduled lunch break when the weather showed no signs of improving and rain continued to drench the covers guarding the Sher-e-Bangla stadium pitch.
Bangladesh, who won the toss and elected to bat, will begin the third day's play on Saturday at 246-8, weather permitting.
More rain has been forecast for the remaining three days of the match.
The first Test ended in a draw in Chittagong last week after bad weather washed out play on the last two days.