The BCCI has been unable to get tickets for the full squad on a single flight.
India's newly-appointed Test vice-captain Ajinkya Rahane departed for the West Indies with a few of his team-mates on Thursday.
The Indian players are leaving for the Caribbean in batches with the BCCI unable to get tickets for the full squad on a single flight.
Rahane made a comeback to the Indian team after a long gap of 18 months in the World Test Championship final against Australia earlier this month.
He was India's best performer in the WTC final with 135 runs in the two innings, which saw him get elevated to the post of Rohit's deputy for the Test series against the West Indies.
Rahane along with Mohammed Siraj, Axar Patel and Srikar Bharat were among the players, who have have left for the West Indies.
Captain Rohit Sharma is expected to join his team-mates directly from Europe, where he is currently holidaying with his family, while Virat Kohli will fly in from the UK.
India's tour of the West Indies begins with the two Test series, starting from July 12, followed by a three-match ODI series and a five-match T20I series.
