The 26-year-old left-armer joins batsman Sohaib Maqsood, fast bowling colleagues Sohail Khan and Ehsan Adil and leg-spinner Yasir Shah, who have all been ruled out with injuries.
The first test starts in Khulna on April 28 with the second match in Dhaka from May 6.
Bangladesh won the recent one-day series 3-0, their first ever series victory over Pakistan, and eased to a seven-wicket win in a Twenty20 international on Friday.
(Writing by Sudipto Ganguly in Mumbai; editing by Ed Osmond)
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