Gayle, 34, has been replaced in the 13-man squad by fellow left-hander Leon Johnson, who is uncapped at Test level.
The big-hitting opener made a swashbuckling 64 in the first Test at St Vincent, including 11 boundaries, and hit the fence twice more in making an unbeaten nine in the second innings to steer the Windies to a 10-wicket win.
Gayle has played in 103 Tests for the West Indies, who will play their 500th game in the five-day format starting Saturday.
West Indies squad: Denesh Ramdin (captain), Sulieman Benn, Jermaine Blackwood, Kraigg Brathwaite, Darren Bravo, Shivnarine Chanderpaul, Kirk Edwards, Shannon Gabriel, Jason Holder, Leon Johnson, Kemar Roach, Shane Shillingford, Jerome Taylor.