"This appears to be an isolated, singular matter, with, at this point, no nexus to terrorism," said Capitol Police Chief Kim Dine.
Law-enforcement authorities identified the woman as Miriam Carey, 34, of Stamford, Connecticut. The authorities spoke on condition of anonymity because they were not authorized to divulge the information publicly.
Stamford Mayor Michael Pavia said the FBI was executing a search warrant at a Stamford address in connection with the investigation. Police officers had cordoned off a condominium building and the surrounding neighborhood in the shoreline city.
The pursuit began when the car sped onto a driveway leading to the White House, over a set of lowered barricades. When the driver couldn't get through a second barrier, she spun the car in the opposite direction, flipping a Secret Service officer over the hood of the car as she sped away, said B.J. Campbell, a tourist from Portland, Oregon.
Then the chase began.
"The car was trying to get away. But it was going over the median and over the curb," said Matthew Coursen, who was watching from a cab window when the Infiniti sped by him. "The car got boxed in and that's when I saw an officer of some kind draw his weapon and fire shots into the car."
Police shot and killed the driver just outside the Hart Senate Office Building, where many senators have their offices. Dine said an officer took the child from the car to a hospital. She is in good condition under protective custody, officials said.
A few senators between the Capitol and their office buildings said they heard the shots.
"We heard three, four, five pops," said Democratic Sen. Bob Casey. Police ordered Casey and nearby tourists to crouch behind a car for protection, then hustled everyone into the Capitol.
The shooting comes two weeks after a mentally disturbed employee terrorized the Navy Yard with a shotgun, leaving 13 people dead including the gunman.
Before the disruption, lawmakers had been trying to find common ground to end a government shutdown. The House had just finished approving legislation aimed at partly lifting the government shutdown by paying National Guard and Reserve members.
Capitol Police on the plaza around the Capitol said they were working without pay as the result of the shutdown.
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Associated Press writers Adam Goldman, Mark Sherman, Philip Elliott, Jesse Holland, David Espo, Alan Fram, Eric Tucker, Brett Zongker, Donna Cassata and Henry C. Jackson in Washington, Michael Melia in Hartford, Connecticut, and John Christoffersen in Stamford, Connecticut, contributed to this report.