Rain at Warner Park led to a delayed start and Bangladesh were 31-0 through 4.4 overs when conditions were deemed unfit for play.
It saw the lone T20 declared a no result ahead of a two-Test series between the teams in September.
Bangladesh had won the toss and opted to bat, making a strong start in St Kitts.
Anamul Haque (19 off 19) and Tamim Iqbal (11 off nine) had made a bright start for the tourists.
But another heavy shower led to umpires calling an end to the clash.