Clare Shillington and Laura Delany both made 37 as Ireland were bowled out for 144 after 47.1 overs of their innings.
Bangladesh replied with 145-3 off 39.1 overs to win with 65 balls to spare, Sharmin Akhter top-scoring with 52.
Ireland must win their remaining two matches against Pakistan and South Africa to maintain qualification hopes.
Ireland retained their one-day international status by making the Super Six, from which the top four qualify for the World Cup this summer.
After being put in to bat by Bangladesh at the Colombo Cricket Club, the Irish women were dealt an early blow as Cecilia Joyce (3) and Kim Garth (0) both went cheaply.
Meg Kendal returned from her hamstring injury to make 16, sharing in a third wicket stand of 45 with Shillington, who struck four boundaries and cleared the ropes twice in an entertaining 37 from 36 balls.
Both fell in quick succession and it was left to skipper Delany and Isobel Joyce (24) to rebuild the innings with a stand of 44.
Having reached 106-4 with 19 overs remaining, Ireland looked set for a total approaching 200, however the innings faltered in the final third, as they slumped to 144 all out.
Jahanara Alam (3-21), Panna Ghosh (2-16) and Khadija Tul Kubra (2-26) were best with the ball for Bangladesh.
Ireland needed quick wickets in the Bangladesh chase, but their attack was blunted by a steady opening stand of 40 between Sharmin Sultana (22) and Sharmin Akhter.
Gaby Lewis (1-31) dismissed Sultana, and when Isobel Joyce ran out Islam for 2, Ireland were back in the contest at 52-2.
However Akhter hit a fine half century from 86 balls, adding 53 with Morgana Hoque, to ensure Bangladesh quickly regained control.
Although Akhter was dismissed by Ciara Metcalfe (1-33), by that stage just 39 were needed, and Hoque (34 not out) in conjunction with Rumana Ahmed (24 not out) steered their side safely home.
Ireland are next in action when they face Pakistan on Friday, before taking on South Africa on Sunday.
Ireland's hopes of qualifying for the World Cup appear remote after suffering a seven-wicket defeat by Bangladesh in their opening Super Six match.