BCB media manager Rabeed Imam said it was the same injury that had ruled Kayes out of the second Test against New Zealand in Christchurch last month.
Bangladesh have flown in middle-order batsman Mosaddek Hossain, who played the ODIs and T20s in New Zealand but was overlooked for the Tests.
Soumya may open
In Imrul’s absence, Soumya Sarkar is likely to open alongside Tamim Iqbal.
Kayes and Iqbal are Bangladesh’s most successful opening combination as they have scored 2205 runs while opening the batting for their side and average an impressive 47.93 as a pair with four century stands.