"There were about 350 people on board when a storm split the steamer into two and so far we have recovered about 40 bodies and an estimated 150 people were either rescued or swam to safety," Assam police chief J.N. Choudhury said.
The double-decker ferry sank in the fast-flowing Brahmaputra river in Assam state, police said.
Indian state-owned broadcaster Doordarshan said more than 100 people were feared killed in the ferry accident.
Witnesses said they saw victims being swept away by the river's strong currents.
The boat was on its way from Dhubri to the adjoining district of Fakirganjan when the accident occurred in late afternoon amid strong currents, Haloi said.
Rescue workers rushed to the site and were struggling to find survivors, but darkness and bad weather were hampering rescue efforts.
"I could see people being swept away as the river current was very strong," Rahul Karmakar, who witnessed the sinking, told AFP.
Dhubri is some 300 kilometres (186 miles) from Guwahati, Assam's largest city.
Karmakar said there were women and children among those on board the ferry, which was carrying farmers, fishermen and other local people.
Boats are a common form of transport in India's remote rural regions and accidents are common due to lax safety standards and overloading.
In one of the last major ferry disasters in India, at least 79 Muslim pilgrims drowned when an overcrowded boat sank in the eastern state of West Bengal in eastern India.
Assam state chief minister Tarun Gogoi said Indian Prime Minister Manmohan Singh had telephoned him and promised to rush disaster response units from the national capital, New Delhi, and other locations.
"Army, Border Security Force and other rescue teams with mechanised boats have moved to the site but nightfall and bad weather are hampering rescue efforts," Gogoi told AFP.
Singh said in a statement that he was "shocked and grieved to know about the loss of lives" and called it a "tragedy."
He said he had given instructions "for all possible assistance to the government of Assam in relief operations and also for assistance from the Prime Minister's National Relief Fund to the families of the deceased."
