The female suspect was shot dead by police officers but is not believed to have returned fire. She is reportedly a 34-year-old dental hygienist from Stamford, Connecticut.
A child, aged around two or three years old, was rescued from the car uninjured following the police chase with the driver of the luxury, black Infiniti.
The driver is believed to have a 'history of mental health issues', ABC reported.
... The pursuit began around 2.15pm when the car sped onto the 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 visiting tourist from Portland, Oregon.
Around a dozen police and Secret Service cars chased the Infiniti toward Capitol Hill.
Matthew Coursen was on his way to a legislative office building when the car sped by him.
He said: 'The car was trying to get away. But it was going over the median and over the curb.
'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.'
Mr Coursen said: 'I thought to myself, ''The car is getting blocked in. The car is going to surrender,'" he said.
'Now the cop has his weapon out. The car kept trying to get away. Then he fired shots.'