The 28-year-old Imrul has played 53 ODIs in which he has scored 1,390 runs with one century and 10 half-centuries. His last one-day international was against Zimbabwe in November 2014.
Haque, 22, dislocated his shoulder while fielding at Saxton Oval. He made two scores of 29 opening the batting in the win against Afghanistan and the defeat to Sri Lanka.
Bangladesh are currently third in Pool A with five points from four matches and will play England in Adelaide on Monday.