Ireland made 129-6 in their 19 overs before heavy rain at the Premadasa stadium prevented the West Indies from starting their innings.
Both teams gained one point each, but the West Indies joined Group B winners Australia in the next round due to a superior net run-rate over the Irish.
The West Indies will be placed alongside defending champions England, New Zealand and hosts Sri Lanka in group one of the Super Eights which starts on Thursday.
Chris Gayle turned star performer with the ball with two wickets as the Ireland innings failed to gain any momentum after the West Indies won the toss and elected to field.
Niall O’Brien made 25 and Gary Wilson scored 21, before both batsmen fell to Gayle’s off-spin.