The shooting happened at about 9:40 a.m. at Sandy Hook Elementary School.
The shooter was killed and apparently had two guns, a person with knowledge of the shooting said. The person spoke on condition of anonymity because the investigation was still under way.
Nearby Danbury Hospital said three patients have arrived from the scene, but their conditions were not known.
The superintendent's office said the district had locked down schools in Newtown, in western Connecticut about 60 miles northeast of New York City.
State police said Newtown police called them around 9:40 a.m.
A photo posted by The Newtown Bee newspaper showed a group of young students - some crying, others looking visibly frightened - being escorted by adults through a parking lot in a line, hands on each other's shoulders.