Authorities say about 29 people were on board the small vessel when it overturned Sunday on the Rupnarayan River, about 50 kilometers from Kolkata, the state capital.
Police officials say fishermen have rescued 11 people.
Boat accidents are common in India, where many vessels are unsafe and overloaded.
Indian officials say some 18 people are missing after an overcrowded boat capsized in a river in West Bengal state.
