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 350 km (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.
A passenger, Hasnat Ali, told local TV channels that about 200 people were travelling inside the boat along with cargo.
Hasnat Ali said he was riding on the top of the ferry with 150 other people when the storm hit, throwing off many of them.
He said he managed to hold on to a log and was rescued by villagers.
The ferry carried no lifeboats or life jackets and was overloaded with people and goods, according to a police officer quoted by Reuters news agency.
Boats are a common mode of transport in the area, which is dotted with small islands and villages along the banks of the river.
Many of the boats are overcrowded with poor or minimal safety features.
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