The wicketkeeper-batsman missed the previous series against New Zealand owing to a paternity leave
Left-arm off-spinner Nayeem Hasan will also be joining the squad.
Tamim Iqbal, however, remains out with an injury.
Shakib had been unable to play several recent matches due to a finger injury.
A total of 13 cricketers make up the squad for the first Test against the West Indies in Chattogram on Nov 22.
Pacers Abu Jayed and Shafiul Islam, batsman Nazmul Hossain Shanto and left-armed spinner Nazmul Islam Apu have been dropped from the squad that faced Zimbabwe.
Bangladesh squad: Shakib Al Hasan (capt), Soumya Sarkar, Imrul Kayes, Mohammad Mithun, Mominul Haque, Mushfiqur Rahim, Ariful Haque, Mahmudullah, Mehidy Hasan Miraz, Mustafizur Rahman, Taijul Islam, Syed Khaled Ahmed, Nayeem Hasan