The Under-23 side were bowled out for 245 in 49.4 overs despite a brilliant six-wicket haul from U-19 pacer Tafiwl Alam Tamim.
At one stage, the U-23 team were struggling at 30 for 3 before recovering through several useful partnerships.
In reply, the U-19 side were 27 for 1 when rain first interrupted play.
The match was later reduced to 43 overs, with the target revised to 161. However, another rain interruption ended the contest with the U-19 side on 99 for 5.
With no further play possible, the match was abandoned.
Bangladesh Under-19 were declared champions based on their superior points tally in the league stage, having collected six points compared to the Under-23 side's five.