The crash happened near the intersection of Brookhurst Street and West Orangethorpe Avenue, where a good Samaritan said he helped the women get out of the wrecked vehicle.
The driver and passenger were said to be speaking and walking unassisted before they were hospitalized.
Firefighters responded to the scene and extinguished the blaze, which left the single-story building significantly damaged.
"We believe alcohol possibly played a factor in the collision," a spokesperson for the Fullerton Police Department said, "but no arrests have been made and it's an ongoing investigation."
A tow truck crew later extracted the car from the building's entrance and removed it from the location.