District of Columbia police chief Cathy Lanier confirmed that the woman, whom she did not identify, died after being shot by police.
Authorities also found a child in the woman's vehicle, but the youngster was not hurt in the incident.
Meanwhile, Capitol police chief Kim Dine said the woman was driving a black Infiniti and tried to break through a barricade at a control point near the White House, injuring a police officer.
Authorities also found a child in the car but the youngster was unhurt
The woman refused to obey the orders of secret service agents to stop and kept driving, sometimes at speeds of up to 112 kph on Pennsylvania Ave., the street that runs between the White House and the Capitol building.
When she got near the Capitol, the woman's car hit a police car and crashed into a barricade, authorities said.
According to Dine, the injured officer has been with the Capitol police for 23 years and is in "good" condition.
The shooting incident occurred while Congress was in session and so authorities immediately implemented a pre-existing security plan and blocked the entrances to legislative buildings for an hour.
Dine denied having any information that would link the incident to a terrorist act.
Police said that they fired at the woman in at least two locations during the chase, in which about 20 police vehicles participated.
The woman reportedly died as she was being transported to a local hospital, but authorities did not say whether she was armed when they opened fire on her.
This incident comes a little over two weeks after a mass shooting on Sep 16 at the US Navy Yard in Washington in which 13 people died, including the shooter, who appears to have had mental problems.