Thirty-one people had swam to safety and six others were rescued by the local people, Malda District Magistrate G Kiran Kumar told PTI.
Among the persons rescued by the locals, five persons were admitted to a Manikchak hospital and one person was shifted to Malda Medical College and Hospital.
Of the nine dead, six were males, two females and one was a 12-year-old boy, he said.
The boat and the boatman were not traceable, he said.
Five rescue teams, including a 35-member Disaster Management Team from Kolkata, were on the job, he said.
Rescue operations were continuing, he said.