The left-hander suffered the injury to the little finger of his left hand and will likely have to sit out the team's three-match one-day international series against Afghanistan at home starting on Sept. 25.
Bangladesh are hopeful the 27-year-old will be fit before England arrive to tour the country for a series comprising three ODIs and two tests, starting on Oct. 7.
"Such injuries take about three to four weeks to heal," Bangladesh team physio Bayzidul Islam said in a statement. "We have time. He should be able to start batting in four weeks."
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(Reporting by Sudipto Ganguly in Mumbai; editing by Peter Rutherford)
