The family of the girl, Tiana Griffith, said she was getting ready to go to a birthday party. Griffith was following her cousin across the street in front of her home on St. Andrews Place near 37th Drive when she was struck by the car.
A neighbor who heard the crash and ran outside said the girl was thrown several feet by the impact.
Griffith was taken to Cedars-Sinai Medical Center, where she was undergoing treatment for a fractured hip, a swollen lung, a deep cut over her eye and bruises.
"She's afraid, she's scared. She doesn't really know what's going on, she just wants to go home," said Griffith's aunt, Evadne White.
Los angles police said the female driver was in a white vehicle that sped away southbound on St. Andrew Place.
Griffith's family is asking the driver to surrender to police.
"She has to look at it from a mother's point of view and her family's point of view," White said. "If this was her child or someone in her family, she would want the same thing in return."
Neighbors said drivers do not slow down in the residential area and they want something to change.
Anyone with information on the hit-and-run was asked to call Los Angeles police at (323) 421-2540.