Mustafizur missed the T20 series against Afghanistan in June due to a toe injury suffered while playing for Mumbai Indians in the Indian Premier League in May.
He also missed a Test series in the West Indies but played a vital role in Bangladesh's 2-1 win in their one-day series with five wickets in three matches.
"He looks fully fit now so we did not consider giving him a rest," said chief selector Minhajul Abedin.
Mustafizur replaces Abul Hasan in the squad.
The first match will be held in Saint Kitts on August 1, with Florida's Lauderhill hosting the next two matches on August 4 and 5.
Bangladesh squad: Shakib Al Hasan (capt), Tamim Iqbal, Soumya Sarkar, Liton Das, Mushfiqur Rahim, Sabbir Rahman, Mahmudullah Riyad, Mosaddek Hossain, Mehedi Hasan, Nazmul Islam Apu, Rubel Hossain, Mustafizur Rahman, Abu Haider, Abu Jayed, Ariful Haque.
First Published: July 29, 2018, 3:09 PM IST