The 22-year-old Haque suffered the injury while fielding during his side's six-wicket victory over Scotland at Saxton Oval in Nelson.
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He had scans at a local hospital and a team spokesman said at the time he had dislocated his shoulder but it was too early to determine how much time he would miss.
It typically takes about three months of rehabilitation on if surgery is not required and officials confirmed on Friday he would take no further part in the tournament.
The 28-year-old Imrul has played 53 ODIs, scoring 1,390 runs at just under 27 with one century and 10 half-centuries.
His last ODI for Bangladesh was against Zimbabwe last November.
Bangladesh have five points from four games and are fourth in Pool A, occupying the final place for the quarter-finals.
They play England on Monday in Adelaide in a match that could decide the fourth qualifier from Pool A. They then travel back to New Zealand to meet the World Cup co-hosts at Seddon Park in Hamilton on March 13 in their final pool match.
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Image: Anamul Haque
Photograph: Andrew Biraj/Reuters
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