Mustafizur was yet to regain his fitness from the injury which also forced him to miss the recent
"Barring a miracle he is unlikely to be fit before the second Test, so we left him out from the squad," Abedin said.
The first Test will be played in Antigua from July 4 while the second and final Test will be held in Kingston, Jamaica from July 12.
Right-arm paceman Abu Jayed, who has played three Twenty20 internationals, earned his maiden call-up to the Test squad.
The squad has several changes from Bangladesh's last Test series in February against Sri Lanka at home which they lost 1-0.
Test Skipper Shakib Al Hasan returned to the squad after missing out on the Sri Lanka series due to injury.
Bangladesh, who are also scheduled to play three ODIs and as many Twenty20 internationals on the West Indies tour, will leave home on June 23.
Shakib Al Hasan (Capt), Tamim Iqbal, Imrul Kayes, Mushfiqur Rahim, Mohammad Mahmudullah, Liton Das, Mominul Haque, Mehidy Hasan, Taijul Islam, Kamrul Islam, Rubel Hossain, Nurul Hasan, Abu Jayed, Nazmul Hossain and Shafiul Islam