The incident started around 4 a.m. Thursday when officers spotted a wrong-way driver on State Route 198 south of Fresno and heading toward NAS Lemoore, authorities said.
CHP chased the vehicle as it crashed through the south fence of the airfield and then crashed into an FA-18E Super Hornet on the south side of the naval base.
The passenger died at the scene. The driver died at a hospital. Their identities were not immediately released.
Officials say the car hit the jet's horizontal stabilizer but have not detailed the damage.
Naval Air Station, Lemoore, built in 1961, has two runways and hosts four Carrier Air Wings.
The Associated Press contributed to this report.