The woman had at least two semi-automatic rifles and a handgun, police said.
The Metropolitan Nashville Police Department began receiving calls at 10.13am on Monday of a shooter at The Covenant School, which teaches children up to sixth grade (about12 years old).
Officers could hear gunfire coming from the school's second floor, police spokesman Don Aaron told reporters.
Two officers from a five-member team shot at her in what Aaron described as a lobby area and she was dead by 10.27am.
"The police department response was swift," Aaron said.
Police later said the shooter was a 28-year-old woman from Nashville, having earlier said she appeared to be a teenager, but have not publicly identified her.
Deadly mass shootings have become commonplace in the United States but a female attacker is unusual.
Only four of the 191 mass shootings since 1966 catalogued by The Violence Project, a non-profit research centre, were carried out by a female attacker.
US President Joe Biden wants Congress to do more to stem gun violence and will address the shooting in remarks later on Monday, the White House said.
Three students were pronounced dead after arriving at Monroe Carell Jr Children's Hospital at Vanderbilt with gunshot wounds, John Howser, a hospital spokesperson, said in a statement.
Three adult staff members were killed by the shooter, police said.
Besides the deceased, no one else was shot, Aaron said.
Students' parents were told to gather at a nearby church.
The Covenant School, founded in 2001, is a ministry of Covenant Presbyterian Church in the Green Hills neighbourhood of Nashville with about 200 students, according to the school's website.
The school serves preschool through sixth graders and held an active shooter training program in 2022, WTVF-TV reported.
Nashville Mayor John Cooper expressed sympathy for the victims and wrote on social media that his city "joined the dreaded, long list of communities to experience a school shooting".
There have been 89 school shootings - defined as anytime a gun is discharged on school property - in the US so far in 2023, according to the K-12 School Shooting Database, a website founded by researcher David Riedman.
In 2022, there were 303 such incidents, the highest of any year in the database which goes back to 1970.
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