To move up from 11th place in the points ranking, Ireland needed to win all three matches in a series against Bangladesh at Chelmsford, the headquarters of the English county Essex.
Even if Ireland wins the series 2-0, they will not be able to overtake South Africa Proteas in the World Cup Super League (WCSL) standings.
Ireland will now compete in a qualifying competition in Zimbabwe from June 18 to July 9, against past champions West Indies and Sri Lanka.
When play was suspended at 4:34 pm local time (1534 GMT), the Irish were 65-3 in the 17th over, chasing Bangladesh’s 246-9 from 50 overs.
Under the Duckworth-Lewis-Stern system for rain-affected matches, a minimum of 20 overs had to be bowled in Ireland’s innings for a result to be declared.
However, the game was called off at 1800 GMT after the umpires determined that the circumstances were too damp to resume play.
Josh Little, fresh from impressing in the Indian Premier League, led Ireland’s assault with 3-61, with Graham Hume and Mark Adair also taking two wickets as Bangladesh were held to a fairly modest score on good ground.
Mushfiqur Rahim celebrated his 36th birthday by leading the Tigers with 61 points in front of a crowd of around 3,000 people, most of whom were Bangladesh fans.
Najmul Hossain Shanto scored 44 points. Ireland, on the other hand, quickly found themselves in difficulty at 27-2 after losing seasoned starter Paul Stirling and captain Andrew Balbirnie.
The series will resume on Friday. The top eight finishers in the three-year-long WCSL competition earn the first slots in the 10-team World Cup.
England, India, New Zealand, Australia, Bangladesh, Pakistan, and Afghanistan have already secured their spots.