The source, speaking on condition of anonymity, said a check of public records showed the suspect, identified as a young US citizen, had a history of driving under the influence.
A CIA spokesperson said earlier that security staff "engaged a person" outside the main gates and then arrested the suspect.
The spokesperson declined to say whether gunfire struck the suspect.
The source familiar with the matter also did not say whether the woman was hit but that she was in stable condition after the incident, which occurred about 4am.
NBC News reported earlier that the suspect was shot, citing a person with knowledge of the matter.
The woman drove into the main entrance through the outbound lane, and when security guards tried to stop her she evaded them and continued toward the gate, drawing their fire, the source told Reuters.
The vehicle never entered the CIA compound and no security officers were hurt, according to the source.
The FBI was investigating the incident, the source said.
The CIA closed the main gate at its Langley compound and directed employees to seek alternate routes.
The shooting incident came after two Israeli embassy staffers were killed by a lone gunman in downtown Washington DC on Wednesday night.
The source said there was no sign of a connection between the two incidents.
