The ferry capsized about 5 p.m. in west Assam's Dhubri district, the Hindustan Times reported.
"The ferry was sailing southeast from Dhubri town to Hatsinghimari. Motorized ferries and country boats tend to be overloaded in these parts," district police Chief Pradip Saloi said from Dhubri.
The vessel was caught in a severe cyclonic storm. Witnesses said they saw passengers being swept away by the river's strong currents.
"The storm sliced through the overloaded boat. We hardly had time to react," said Qasem Ali, a survivor.
So far, 68 people have been confirmed dead and only 38 bodies had been recovered, police said. About 100 people swam to safety.
Rescue teams were looking for survivors and bodies, but low light and bad weather hindered their efforts.
Meanwhile, a government spokesman said an investigation had been started into the cause of the mishap.
"The intention is to fix responsibility and ensure that the number of passengers on ferries is regulated," he said.