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.
It wasn't clear how many people were injured at Sandy Hook Elementary School in Newtown. A dispatcher at the Newtown Volunteer Ambulance Corps said a teacher had been shot in the foot and taken to Danbury Hospital.
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.