The woman was not shot, Washington Metropolitan Police spokesperson Rachel Reid told the BBC, and no injuries have been reported.
She was taken into custody and the incident prompted a lockdown at one of the Congress buildings.
The incident follows driving attacks last week in London and Brussels.
Capitol Police spokeswoman Eva Malecki said the suspect is a woman, and the incident is "criminal in nature with no nexus to terrorism".
The incident occurred after officers observed an "erratic and aggressive driver" and tried to pull her car over.
The driver made a U-turn, nearly striking several officers in the process.
No motivation is known, and the woman has not been identified.
Hearings on Capitol Hill are continuing as normal, and tourists are being allowed to return to the area.