Police said the car sped down Pennsylvania Avenue toward the Capitol, where security vehicles stopped it at Garfield Circle.
The woman slammed the car into reverse, crashing into a police cruiser, and tried to get away. At that point officers began firing, a witness said.
Dramatic video footage by a videographer for Alhurra TV, a Middle Eastern news outlet financed by the U.S. government, showed the black vehicle then speeding around a nearby traffic circle with a police car in close pursuit and then heading away. The car crashed into more security barriers a few blocks later, witnesses said.
More shots were fired after the vehicle stopped, and the woman was hit several times, said Metropolitan Police Department Chief Cathy Lanier. Carey was later pronounced dead, Lanier said. Two officers were injured.
A Capitol Police officer whose vehicle crashed during the chase was hurt, authorities said. The officer was released from a hospital Thursday night. The Secret Service did not release information about its injured agent.
Chaos and a child in the car
Inside the woman's car was the 1-year-old child, who was not harmed. The child was taken into protective custody, officials said. Officers didn't know there was a child inside the woman's car during the chase, officials said. Also, the early investigation revealed that there was no evidence that the woman had a gun or fired a shot.
The bedlam from the fatal chase reverberated throughout a U.S. Capital already shaken by the recent mass shooting at the Navy Yard in the city and on edge due to tensions over the showdown over shutting down the federal government.
Authorities locked down the Capitol building and other government facilities in the area.
House and Senate sessions were immediately suspended, with legislators ordered to take cover and keep away from windows. Police also closed Pennsylvania Avenue in front of the White House.
Sirens blared as people in and around government office buildings reported hearing gunshots. Bystanders hid in fear.
Shemaiah Ofori-Attah and her husband, Edmund, at first thought the speeding black car and sirens were part of a motorcade.
"Then when we heard the gunshots we knew this was something serious, so we just dropped to the ground," she said.
Danny Farkas, the Alhurra videographer, captured the scene. He said he had a fleeting thought that perhaps the driver had explosives in the car.
"I was surprised at the movie-like quality of what was going on in front of me," he told CNN's "New Day."