Mithun and Nasir were not part of the Bangladesh squad that drew 2-2 with Zimbabwe in the recent series in Khulna.
Chief selector Faruque Ahmed said they have been picked as "back-up" to the regular players.
"More or less we have an idea about our best 11 players. We thought they have the potential to be the next best," Faruque told a press conference.
Wicketkeeper-batsman Mithun played his last T20 international against the West Indies in August 2014 while Nasir was rested during last month's series against Zimbabwe.
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Batsman Mushfiqur Rahim and left-arm paceman Mustafizur Rahman also return to the squad after missing the last two matches against Zimbabwe due to injury.
Bangladesh will play in the qualification Group A alongside Ireland, the Netherlands and Oman.
The top team from the group will then enter the main draw to take on the eight leading cricket nations in matches starting on March 15.
Squad: Tamim Iqbal, Soumya Sarkar, Mohammad Mithun, Shakib Al Hasan, Mushfiqur Rahim, Sabbir Rahman, Mashrafe Mortaza (capt), Mahmudullah Riyad, Nasir Hossain, Nurul Hasan, Arafat Sunny, Mustafizur Rahman, Al-Amin Hossain, Taskin Ahmed and Abu Hider.