The Hartford Courant newspaper, citing unidentified police sources, reported "multiple" people, including children, were killed at Newtown's Sandy Hook Elementary School.
The Courant said among those shot were children from kindergarten through Grade 4, though it was unclear if any children had died.
The shooter was killed and apparently had two guns, a person with knowledge of the shooting told The Associated Press. The person spoke on condition of anonymity because the investigation was still under way.
A dispatcher at the Newtown Volunteer Ambulance Corps said a teacher had been shot in the foot and taken to Danbury Hospital.
Stephen Delgiadice said his eight-year-old daughter heard two big bangs and teachers told her to get in a corner. His daughter was fine.
"It's alarming, especially in Newtown, Connecticut, which we always thought was the safest place in America," he said.
The superintendent's office said the district had locked down schools in Newtown, in western Connecticut 96 kilometres northeast of New York City.
State police said Newtown police called them around 9:40 a.m. local time.
A photo posted by The Newtown Bee newspaper showed young students — some crying and looking frightened — being escorted by adults through a parking lot in a line, hands on each other's shoulders.
Emergency vehicles surrounded the school in western Connecticut and parents were seen running toward the building as a helicopter flew overhead.