Gayle, who has two triple centuries in the longest format, played the last of his 103 Test matches almost five years ago but expressed his desire during the World Cup to don the white jersey for the West Indies one final time.
The 39-year-old is one of the prolific run-scorers for his country in Test cricket, having accumulated 7,214 runs at an average of 42.18 with his career-best 333 coming against Sri Lanka in 2010.
Gayle has been restricted to limited-overs cricket and T20 franchise competitions around the globe in recent years.
The remaining two ODIs in the ongoing three-match series between the two sides could well be Gayle's final international appearances.
Alzarri Joseph, who was part of the squad that defeated England at home earlier this year and registered the best bowling figures in his debut match in the Indian Premier League (IPL), will not partake in the Test series due to an injury incurred in the summer.
Left-arm spinner Jomel Warrican is the other player to be left out from the victorious Test squad.
Warrican has been replaced with Rahkeem Cornwall, who boasts 260 wickets from 55 first-class games and was rewarded for his splendid performances in the regional one-day tournament.
"Rahkeem has been performing consistently over a long period of time and has proven to be a match-winner, so we believe his elevation to the Test squad is merited at this time," said the interim selection panel chief Robert Haynes.
Meanwhile, Keemo Paul has been able to retain his spot in the squad despite being drafted in as a replacement for captain Jason Holder, who was suspended from the final Test against England for maintaining a slow over-rate.
"Alzarri is undergoing remedial work and we are monitoring his recovery, but we do not think he is ready yet to last five days of a gruelling Test match," added Haynes.
Jason Holder (c), Kraigg Brathwaite, Darren Bravo, Shamarh Brooks, John Campbell, Roston Chase, Rahkeem Cornwall, Shane Dowrich, Shannon Gabriel, Shimron Hetmyer, Shai Hope, Keemo Paul, Kemar Roach.