Match officials called an end to the day at around 2:00 pm local time (0800 GMT) with the weather showing no signs of improvement.
Fifteen wickets fell in the first day with the tourists trailing by 117 after being held to 55-5 at stumps.
Bangladesh opted to bat first and were all out for 172 runs in their first innings.
The hosts lead the two-match series 1-0 after a 150-run win in the opening Test in Sylhet.