The 35-year-old Gayle was the most notable omission from the squad to be led by Dwayne Bravo in the five-match series starting October 8 in Kochi.
The Caribbeans have brought in batsmen Marlon Samuels and Dwayne Smith, and fast bowler Jerome Taylor for the series.
Other players who have been left out are batsman Kirk Edwards and left-arm spinner Nikita Miller.
Samuels and Smith had missed the series against New Zealand Bangladesh earlier this year. Taylor, however, is making a return after four years of struggle with injuries.
Dwayne Bravo (capt), Darren Bravo, Jason Holder, Leon Johnson, Sunil Narine, Kieron Pollard, Denesh Ramdin (wk), Ravi Rampaul, Kemar Roach, Andre Russell, Darren Sammy, Marlon Samuels, Lendl Simmons, Dwayne Smith, Jerome Taylor.