Umpires Daryl Harper and Billy Doctrove abandoned play at noon (0600 GMT) after heavy rain, which waterlogged the Ruhul Amin Stadium, did not relent.
Already 173 overs have been lost over three days because of the rains which are forecast to continue for the whole week.
Just 20 overs were bowled on Saturday during which India took their first innings total to 384-6 with Sachin Tendulkar and Sourav Ganguly scoring centuries.
Inclement weather over this port city had also forced last Tuesday's third and final one-day international to be abandoned without a ball being bowled.
With the Test now almost certain to end in a draw, the series hangs on the second and final Test to be played in Dhaka from May 25.