The third match of the tri-nation series with the West Indies being the other team was scheduled for Thursday.
But the toss for the match at Malahide had initially been delayed due to a wet outfield following several bouts of rain since the morning.
Although the rain had stopped, the covers remained on the pitch.
The umpires declared the match abandoned without a ball being bowled around 2:15pm local time.
The Tigers had to cancel their practice session on Wednesday due to inclement weather.
Hosts Ireland were eyeing a comeback after successive ODI defeats, the last to the West Indies in the first match of the series.
Bangladesh are sitting pretty at the top of the table with six points in two matches and will take on the Caribbeans next Monday.
The West Indies are second with five points, including a bonus point for the huge win over Ireland in the first match.
The hosts, who have earned two points thanks to the rains, will face the West Indies on Saturday.