The boat went down in the Ganga River about 7:30 a.m. in Malda district of West Bengal State after it left Dharampur, the Press Trust of India news agency reported.
Four bodies, including that of a woman, had been retrieved by local rescuers. Eight people were rescued and a search was on for those missing.
The Hindustan Times reported there were about 70 passengers on the boat and quoted local people as saying it was overloaded. The report said there were strong winds causing turbulence in the river.