After suffering a golden duck (hit wicket) on debut, he was out in the same manner in the second test.
Ambris was then struck on the arm in the second innings and retired hurt.
Left-arm orthodox spin bowler Jomel Warrican has also been named for the India tour.
Warrican will provide a second slow bowling option alongside leg-spinner Devendra Bishoo as the visitors seek to end a poor recent record in India.
They have not won a test there since 1994.
Warrican, a 26-year-old from St. Vincent who is also handy with the bat, has played four tests, most recently in early 2016.
The Windies are coming off a moderately successful home stint. They drew a three-test series with Sri Lanka 1-1, before thumping Bangladesh in two tests.
The first test against India will be held in Rajkot from Oct. 4-8, with the second in Hyderabad from Oct. 12-16.
West Indies squad:
Jason Holder (captain)
Sunil Ambris
Devendra Bishoo
Kraigg Brathwaite
Roston Chase
Shane Dowrich
Shannon Gabriel
Jahmar Hamilton
Shimron Hetmyer
Shai Hope
Alzarri Joseph
Keemo Paul
Kieran Powell
Kemar Roach
Jomel Warrican
(Reporting by Andrew Both in Cary, North Carolina; Editing by David Holmes)
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