Gayle, who had missed the final Test against Bangladesh earlier this month due to a lower-back injury, will also miss the limited-overs leg of the India tour.
"My recovery has been coming on nicely, and I expect to be fully fit and ready in time for the Test series," Gayle was quoted as saying by the 'Jamaica Gleaner'.
The explosive batsman added, "The injury is the same one that has been affecting my back in recent times, but so far it has been coming on well. I have been able to give it some rest and as each day progresses, it keeps getting better and better."
In the home Tests this summer, Gayle made three half-centuries in four games.
One of the most experienced campaigners in the West Indies squad, Gayle has played in 103 matches.
He has scored 7,214 runs at an average of 42.