Officials say the woman had a child in the car with her who was not injured and that at least one Capitol Hill police officer was injured in the incident but apparently not shot, media reports said.
The US Capitol was placed on lockdown for a short while after the initial reports of shots fired in the vicinity.
Capitol Police said it appeared to be an isolated incident not related to terrorism.
As a warning alarm sounded inside the Capitol after the reports of gunfire, the US House of Representatives abruptly went into recess and the Senate also suspended business, The Associated Press reported.
The incident happened in the midst of a US government shutdown as Congress has been involved in a heated debate over funding the government.
US President Barack Obama was briefed about the reports of gunfire, according to a White House statement.