The plane's fuselage crashed through one roof, and its left wing lodged in a second home.
It was unclear whether the injured people were on the ground or in the plane, Gregor said. Their conditions were not immediately available.
The crash did not cause a fire, according to Downey fire Capt. Lonnie Kroom.
The flight originated at Montgomery Field in San Diego and was heading for Compton, Gregor said.
The Cessna is owned by Eureka International of Carson City, Nev., Gregor said.
Compton/Woodley Airport is home to several aviation clubs but does not have an air traffic control tower.