Police said about 150 people had been rescued or swam to safety while at least 100 more were missing.
The death toll was likely to rise, Assam Chief Minister Tarun Gogoi said.
Lax safety standards mean ferry accidents are common on the river, but this is one of the worst disasters.
The accident happened in the remote district of Dhubri, about 350km (215 miles) west of Assam's main city, Guwahati.
The ferry capsized and broke into two pieces during the storm, police said.
Witnesses said many passengers were swept away by the river's strong current after the boat broke up.
Officials said they believed many bodies had been carried by the river downstream to neighbouring Bangladesh.