Heavy downpours washed out the morning session and rain was pouring again in the afternoon, prompting the match official to abandon play after lunch.
When and if the action resumes on Saturday, Bangladesh will continue on 246 for eight after opting to bat first at Mirpur's Shere Bangla National Stadium.
The weather also intervened in the drawn first test in Chittagong with only 221 overs bowled as rain curtailed play on the second and third days before washing out the last two days.
While the rain in Dhaka compromises the prospect of a result again, Bangladesh, who stunned the Proteas in the one-day series, are unlikely to mind a drawn series against opponents who sit eight places above them at the top of test rankings.
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
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