The baby had been near the porch of a vacation bungalow with family members when the black bear approached, said Fallsburg Police Chief Brent Lawrence.
The mother shuttled her 4- and 2-year-old children inside, Lawrence said. When she returned outside, the infant was gone.
Witnesses told police the young bear had little Ester Schwimmer in its mouth as it ambled into dense woods 20 feet from the bungalow.
"It may be the first season that it may have been on its own, and it may very well have perceived this infant as a food source," Lawrence said. "I wouldn't categorize it as an attack - as far as a running, snarling attack."
Isaac Abraham said people desperately tried to save the girl.
"People started chasing the bear, throwing rocks at it," he said.
The bear dropped the infant, but she had severe injuries to her head and neck, and was pronounced dead at a hospital, Lawrence said.
Officers with the Department of Environmental Conservation and local police tracked the bear into the woods and shot it.
Ward Stone, the state's chief wildlife pathologist, said it was the first time he could remember a black bear killing a human.
"In all my many years, 34 summers, we've had them eat birdseed, get into trouble eating dog food in people's yards but black bears are just not noted for attacking humans," Stone said.
The girl's family was from the New York City borough of Brooklyn, officials said.
The attack happened in the Catskills region about 70 miles northwest of New York City, in the heart of what is known as the Borscht Belt. Big hotels and bungalows attracted thousands of visitors each summer, many of them Jewish families from New York City.