Jayawardene, 35, who is Sri Lanka’s highest run-getter in Tests, dislocated a finger in his left hand while fielding during a domestic first-class match in Colombo on Sunday.
Scans of the injury have been sent to Australia for further analysis, Sri Lanka Cricket said in a statement, adding that the batsman could be out of action for four to six weeks.
Bangladesh are due to play two Tests, three one-dayers and one Twenty20 international during their month-long tour of Sri Lanka in March.
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