Chula Vista police Capt. Gary Wedge told The Associated Press that the agent fired after being driven several hundred yards on the hood of the car. The woman was later identified in a police statement as Valeria Alvarado.
A witness said he saw a man in civilian clothes on the hood of a black car aiming a gun at the windshield. The witness said the man pulled the trigger, and other plainclothes agents approached the car soon after.
The shooting occurred about five miles north of the Mexican border as agents were looking to serve a felony warrant in the area to someone other than Alvarado, Border Patrol Deputy Chief Rodney Scott told U-T San Diego.
Scott said the agent was stuck atop the car as Alvarado drove.
"Fearing for his life, he discharged his weapon to get the vehicle to stop," Scott said. No other agents fired.
Alvarado was declared dead at the scene, and the agent was taken to a hospital. The extent of his injuries remains unclear.
Family members said Alvarado grew up in Chula Vista where the shooting took place but had been living about five miles away in the Southcrest neighborhood of San Diego. They did not know why she was in her former hometown. Friends say Alvarado was a housewife and mother of five children ranging from ages 3 to 17 who went by the name Monique.
The person named in the warrant the agents were serving was not apprehended, officials said.
The Associated Press contributed to this report.