It is the country's third outbreak since 2006 and the first since India, home to 1.1 billion people, declared itself free of the disease last November.
"The samples sent to the laboratory have tested positive for bird flu. It is the H5N1 strain," said agriculture ministry spokesman Manoj Pandey.
The poultry deaths were reported from farms in the state's Morgram village, in Birbhum district, 125 kilometres (75 miles) from the state capital Kolkata.
"Blood samples of the dead chickens in the village tested positive," said West Bengal's minister for animal resources development Anisur Rahaman.
An isolation centre had been opened in a hospital near the affected village and 300 health workers had been sent with medicines and protective gear, he said.
"Authorities have ordered the culling of the chickens and all poultry within five kilometres (three miles) of Margram village. The government will pay compensation," Rahaman said.
"Health officials have been asked to launch a campaign over public address systems and distribute leaflets," he said, adding "panic has gripped the village."
The Indian government, meanwhile, said 35,525 poultry in 102 villages of Birbhum as well as 288 birds in a state-run poultry farm in Dinajpur district died in the past seven days but added the outbreak appeared to be localised.
The state government has set up 60 "rapid response teams" for the culling and protective gear for 5,000 personnel was being sent to West Bengal.
"The state government has been also advised to seal its border with neighbouring countries and also the affected areas so that there is no movement of animals across these borders," the Indian government said in a statement.
Humans are typically infected by coming into direct contact with infected poultry, but experts fear the deadly H5N1 virus may mutate into a form easily transmissible between humans.
Wild migratory birds have been blamed for the global spread of the disease, which has killed more than 200 people worldwide since 2003.
India's state of West Bengal borders densely populated and impoverished Bangladesh, where authorities have been struggling to contain an outbreak of the virus.