The mishap occurred in the Bangladesh team hotel in Birmingham on June 15 after the semi-final loss to India in the Champions Trophy.
Bangladesh Cricket Board physician Monirul Amin said Rubel underwent surgery today and would need four to six weeks off to recover.
"We hope he will be fine after that period, and make himself available for selection for the Australia series," Amin told AFP, referring to the first of two Tests starting late August.
Bangladesh progressed to the semi-final of the 50-over tournament for the first time in their history, but were crushed by India in a nine-wicket thumping.