Zimbabwe and Sri Lanka will also take part in the tournament, Bangladesh's first ODI competition at home in more than a year. It will begin in Dhaka on January 15.
"Taskin and Soumya both were dropped for their poor form. They will play in the BCL (a franchise-based first-class competition) to improve their skills," chief selector Minhajul Abedin told a press conference.
Soumya has been a regular face in the Bangladesh squad for all three formats since making his international debut in 2014 but paid the price for a prolonged spell of poor form.
The left-hander played just one ODI in the South Africa tour last October and scored only eight runs.
Fast bowler Taskin also fared poorly in South Africa, picking up two wickets in three ODIs.
Left-arm fast bowler Mustafizur Rahman returns to the side after missing out on Bangladesh's last one-day series in South Africa with a twisted ankle.
Mustafizur was joined by batsmen Anamul Haque and Mohammad Mithun, paceman Abul Hasan and spinner Sunzamul Islam in the squad, which features several changes from the South Africa series in October.
Bangladesh failed to win a single game in South Africa in any format.Head coach Chandika Hathurusingha resigned in the middle of the series, though his decision was only made public in December.
The Bangladesh Cricket Board also sacked Test captain Mushfiqur Rahim and his deputy Tamim Iqbal and replaced them with Shakib Al Hasan and Mahmudullah respectively.
The ODI squad also had no room for batsman Liton Das, who played all three ODIs in South Africa but could score only 41 at 13.66.
But left-arm spinner Sunzamul returned after playing his only ODI in Ireland in June.
Bangladesh will face Zimbabwe in the opening match.
The tri-nation tournament will be followed by a home series against Sri Lanka featuring two Tests and two Twenty20 Internationals.
Squad: Mashrafe Mortaza (capt), Shakib Al Hasan, Tamim Iqbal, Imrul Kayes, Anamul Haque, Mohammad Mahmudullah, Mushfiqur Rahim, Sabbir Rahman, Nasir Hossain, Mohammad Mithun, Mehedi Hasan, Mustafizur Rahman, Abul Hasan, Rubel Hossain, Mohammad Saifuddin, Sunzamul Islam.
First Published: January 7, 2018, 5:46 PM IST