A health official and four members of a family have died from the illness since early April, said Mohan Basu, a doctor in West Bengal state's Nadia district.
The Nipah virus is usually spread by fruit bats or pigs. There have been no known cases of human-to-human infection, according to the World Health Organization.
The last major Nipah outbreak occurred in Malaysia, where 265 people were infected in 1998-99. The virus was then blamed for 105 human deaths.
Nearly a million pigs, believed to have spread the disease, were slaughtered before the Malaysian outbreak was controlled.
The virus, which causes encephalitis, is lethal in about 50 percent of infected humans. No drugs have proven effective against it.
Nadia is 120 kilometers (75 miles) from West Bengal's capital of Calcutta and borders Bangladesh, which had a Nipah outbreak in 2004.
"Initially we thought that the cases were of dengue (a mosquito-borne viral disease), but a test later confirmed that it was Nipah virus that caused the deaths," Basu said.
The outbreak was confirmed by the region's senior health official, Nipati Roy. The virus was found in samples that were sent to the National Institute of Virology.
"We are sending streams of blood samples taken from bats and pigs and even household pets," Basu said. "We are keeping a close surveillance."
Basu said he suspected that the virus had been spread by fruit bats in Nadia, and that residents have been warned to avoid the flying mammals.