Sixteen members of the National Security Guards (NSG), who look after VIP security in India, will cover Rahul Dravid's side during the 48-day tournament, the reports said.
Security officers have in the past carried out pre-tour checks in various countries where the Indian team was due to play, but this is the first time Indian commandos will be deployed to protect the players.
"The decision, taken early this week by the government, comes after a security assessment that terror groups could target the Indian team, which was followed by a formal request from the West Indies," said the Indian Express.
An Indian security assessment said "there were chances of terror groups targeting the tournament, particularly at venues where the Indian team is slated to play," the newspaper said.
"The matter was taken up with the Caribbean authorities, who felt such elaborate security cover may not be possible without assistance."
The newspaper quoted government sources as saying that West Indian officials indicated they did not have the expertise to deal with such terror threats and urged India to help "as the Indian team was identified as a prime target."
The commandos will be located in Jamaica, where India play warm-up matches, and in Trinidad, where the team's preliminary matches will be held, the paper added.
An Indian cricket board official declined to comment on the report.
Two senior players, Sachin Tendulkar and Sourav Ganguly, already have NSG cover in India following threats to their life from militant groups.