Bangladesh stunned England by 15 runs in Adelaide to knock Eoin Morgan's team out of the tournament and secure their third victory in five matches.
"Bangladesh's victory means Sri Lanka has secured the fourth and final spot from Pool A in the last eight stage of the tournament," the International Cricket Council (ICC) said.
Tournament hosts New Zealand and Australia, the top two teams in the pool, had already secured their places in the quarter-finals.
In Pool B, only holders India have secured their quarter-final place so far, winning all four games.
(Reporting by Amlan Chakraborty in New Delhi; editing by Ed Osmond)
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