After the Test series, Nazmul Hossain Shanto and Abu Jayed Chowdhury will remain in the Caribbean islands for the ODI matches.
Nazmul Islam Apu and Abu Hider Rony from the T20 squad have also been called up for the ODI series.
Injured pacer Mustafizur Rahman and Mosaddek Hossain, who have been dropped from the Test squad, have also been named in the ODI squad announced on Tuesday.
Imrul Kayes, Mohammad Mithun, Abul Hasan, Mohammad Saifuddin and Sunzamul Islam, who were in the ODI squad for the tri-nation series against India and Sri Lanka in January, have been dropped.
Nasir Hossain has been sidelined with a knee surgery for long.
Sabbir Rahman, who failed to cross 40 runs in any of his last 11 ODIs but scored a career-best 165 against Sri Lanka A in January, has been included in the squad.
The first two of the three-match series will be played in Guyana on July 22 and 25 and the last one in Saint Kitts on July 28.
Those who are not in the Test squad, including Captain Mashrafe Bin Mortaza, will leave Dhaka on July 14.
Full squad:
Mashrafe Bin Mortaza (captain), Shakib Al Hasan (vice-captain), Tamim Iqbal, Anamul Haque, Liton Kumar Das, Mushfiqur Rahim, Sabbir Rahman, Mahmudullah, Mosaddek Hossain, Nazmul Islam Apu, Nazmul Hossain Shanto, Mehidy Hasan Miraz, Rubel Hossain, Mustafizur Rahman, Abu Hider, Abu Jayed Chowdhury.