The crash occurred shortly after 3 p.m. near Lorena Street and Cesar Chavez Avenue, according to the Los Angeles Fire Department.
Video from AIR7 showed a white vehicle on the sidewalk near Los 5 Puntos restaurant. The area was cordoned off with crime-scene tape.
Neighbors said the driver struck a family having lunch on the sidewalk and was later taken into custody.
Witness Joe Diaz said a woman suffered severe leg injuries after being struck, while her daughter was shaken but not seriously hurt. Diaz also said a passerby was injured when a trash can was pushed into him during the crash.
First responders said a man and a woman were taken to a hospital. Their conditions were not immediately known.
Neighbors said the intersection is prone to accidents.
The cause of the crash remains under investigation.