Rookie paceman Abul Hasan, who has played four Twenty20 internationals, will also be hoping to make his Test debut after being included in the squad on Thursday.
Gazi's selection was a reward for his impressive performance in the ongoing National Cricket League where the 21-year-old claimed 11 wickets in two matches, including a hat-trick, and hit a century.
"He played very well in the National Cricket League, took few wickets and scored a century, so we thought this is the perfect time to give him the break," chief selector Akram Khan said.
"Also he is an off-spinner, as you all know West Indies team have plenty of left-handed batsman, so we needed someone like him."
Pace bowler Rubel Hossain returned to the side, led by stumper Mushfiqur Rahim, after a long injury lay-off but there was no such joy for former captain Mohammad Ashraful, who was replaced by Naeem Islam.
Khulna hosts the second and final Test from November 21.
Squad: Mushfiqur Rahim (captain), Mahmudullah, Tamim Iqbal, Shakib Al Hasan, Zunaed Siddique, Shahriar Nafees, Naeem Islam, Nazimuddin, Nasir Hossain, Elias Sunny, Shahadat Hossain, Rubel Hossain, Abul Hasan, Shohag Gazi.