The decision follows after senior batsmen Tamim Iqbal and Msuhfiqur Rahim are carrying minor injuries.
Mithun has already played three One-Day Internationals and 12 T20Is for Bangladesh and was also part of the side that lost to Sri Lanka in the recently concluded tri-series final in Dhaka.
Earlier, uncapped spinner Nazmul Islam was added to the Bangladesh squad as a replacement for Shakib Al Hasan, who failed to recover from his finger injury and Mahmudullah was handed over the reins of the side for the first game.
Following the first game on Thursday, the two teams will meet once again on Sunday for the second and final game to be played in Sylhet.
Bangladesh squad for first T20I:
Tamim Iqbal, Soumya Sarkar, Mushfiqur Rahim, Mahmudullah (captain), Sabbir Rahman, Mustafizur Rahman, Rubel Hossain, Mohammad Saifuddin, Abu Hider, Abu Jayed, Ariful Haque, Mahedi Hasan, Zakir Hasan, Afif Hossain, Nazmul Islam, Mohammad Mithun
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