If confirmed, it would be one of the worst mass shootings in U.S. history. It comes after a series of shooting rampages in the United States this year that have killed multiple victims.
The principal and school psychologist were among the dead, CNN said.
A law enforcement official says the suspect in the U.S. school shooting is 24-year-old Ryan Lanza and that his younger brother is being held for questioning as a possible second shooter. The law enforcement official says the boys' mother, Nancy Lanza, works at the Connecticut school as a teacher.
The official also said Ryan Lanza's girlfriend and another friend are missing in New Jersey.
The official said the suspect is dead from a self-inflicted gunshot wound.
The official spoke on the condition of anonymity because the source was not authorized to speak on the record about the developing criminal investigation.
There were unconfirmed reports of a second shooter after witnesses reported hearing dozens of shots, CBS reported.
Sandy Hook Elementary School teaches children from kindergarten through fourth grade - roughly ages 5 to 10.
“It was horrendous,” said parent Brenda Lebinski, who rushed to the school where her daughter is in the third grade. “Everyone was in hysterics - parents, students. There were kids coming out of the school bloodied. I don't know if they were shot, but they were bloodied.”
Television images showed police and ambulances at the scene, and parents rushing toward the school. Parents were seen reuniting with their children and taking them home.
“This is going to be bad,” a state official told Reuters, requesting anonymity because the scope of the tragedy remained uncertain.
All Newtown schools were placed in lockdown after the shooting, the Newtown Public School District said.
Lebinski said a mother who was at the school during the shooting told her a “masked man” entered the principal's office and may have shot the principal. Lebinski, who is friends with the mother who was at the school, said the principal was “severely injured.”
Lebinski's daughter's teacher “immediately locked the door to the classroom and put all the kids in the corner of the room.”
Danbury Hospital, about 11 miles west of the school, had received three patients from the scene, a hospital spokeswoman told NBC Connecticut. The mayor of Danbury, Mark Boughton, told MSNBC: “They are very serious injuries.”
A girl interviewed by NBC Connecticut described hearing seven loud “booms” as she was in gym class. Other children began crying and teachers moved the students to a nearby office, she said.
“A police officer came in and told us to run outside and so we did,” the unidentified girl said on camera.
One child was carried from Sandy Hook Elementary School by a police officer, and the child appeared to have been wounded, the town's weekly newspaper, the Newtown Bee, said on its website.
Connecticut State Police said its officers were at the scene with local police but provided no additional details. The emergency call to police occurred at 9:41 a.m., state police said.
An individual answering the phone at the Newtown Police Department declined to comment.
Newtown, with a population about 27,000, is in northern Fairfield County, about 45 miles southwest of Hartford and 80 miles northeast of New York City.
Sandy Hook is one of four elementary schools in the district.
The United States has experienced a number of mass shooting rampages this year, most recently in Oregon, where a gunman opened fire at a shopping mall on Tuesday, killing two people and then himself.
The deadliest attack came in July at a midnight screening of a Batman film in Colorado that killed 12 people and wounded 58.