Haque suffered the injury in the 31st over of Scotland's innings of 318 for eight in their World Cup Pool A clash at Saxton Oval in Nelson.
The 22-year-old dived to stop a ball on the boundary and got to his feet with his right arm hanging limply by his side. He left the field and went to hospital for scans.
"Anamul has been diagnosed with a right AC joint strain, grade three," a team spokesman told reporters in Nelson after Bangladesh scored 322 for four to record a six-wicket victory.
"The team management is in consultation with local medical experts on this particular injury and we will decide on the best possible management.
"At the moment we're not able to say how long it might take for him to recover."
A Grade Three injury results in a total separation of the shoulder joint and typically can take up to three months of rehabilitation if the person does not require surgery.
Haque's absence from the lineup did not prevent Bangladesh from calmly chasing down the total with Tamim Iqbal top-scoring with 95 and Shakib Al Hasan (52 not out) and Sabbir Rahman (42 not out) guiding Mashrafe Mortaza's side home with 11 balls to spare to cap off the perfectly timed run chase.
"The coach said that we should bat like we're batting first and not to think about the total," Iqbal said of how they approached the run chase.
"We chased down a similar kind of score two or three years back against Zimbabwe and we batted in a similar way.
"So rather than thinking about the scoreboard that's extra special, we were just enjoying the wicket.
"The wicket was fantastic and the outfield was really quick. So we didn't have to do too much because if we were timing the ball, then the ball was flying (and) that made it easy for us."
The victory moved Bangladesh to five points in Pool A and they now head to Adelaide for a showdown with England, who have just two points.
Mortaza said Thursday's game had been good preparation for Adelaide and their final game against New Zealand.
"Our bowlers did not bowl well, but our batsmen got runs, especially with a big match coming up," Mortaza said.
"We will try our best against England, and if not them, then New Zealand definitely," he said.

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