Kumar, who missed a recent one day series in South Africa due to injury, underwent a fitness test in Bangalore on Monday but his chances of figuring in the showpiece event looked bleak.
"(Kumar) has not fully recovered. His injury has taken more time to heal than it was expected," the Indian Express quoted an unnamed selector as saying. "The problem is that it's his bowling arm which is injured, so we can't take a risk."
Paceman Shanthakumaran Sreesanth is thought likely to take Kumar's place in the 15-man squad. The 24-year-old Kumar, known for his shrewd variation, has so far bagged 57 wickets in 48 one-day internationals.
India, knocked out in the first round of the 2007 edition in the Caribbean, open their campaign against Bangladesh in Dhaka on February 19.