The 21-year-old has not played a Test since his debut series against South Africa in 2015 after suffering a series of injuries. He underwent surgery on his shoulder last year.
While he made a brief return to the limited-overs side against New Zealand at the turn of the year, he was not deemed fit enough to withstand the rigours of a five-day Test match.
Bangladesh are due to play two Tests against the Sri Lankans -- one in Galle from March 7-11 and another in the capital Colombo which starts on March 15 and will be their 100th Test match.
The selectors also handed fast bowler Rubel Hossain a recall after he was ignored for Bangladesh's recent defeat in a one-off Test against India, meaning there are five pacemen in the squad.
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"We think we would require an extra pacer in testing conditions in Sri Lanka," said chief selector Minhajul Abedin.
Opening batsman Imrul Kayes was not named in the squad after he failed to recover sufficiently from a thigh injury picked up in India. But Abedin said he could be called up for the second Test if he regains fitness.