Singleton, 39, immediately stopped his car and waited for police to arrive after the accident Thursday night in the city's Jefferson Park neighborhood, said Officer Jason Lee, a police spokesman.
"Mr. Singleton stopped and identified himself as required by law and was not under the influence of drugs or alcohol," Lee said. "He was questioned and released."
The woman was taken to a hospital where she was pronounced dead Friday morning, Lee said. She was identified as Constance Russell, 57, of Los Angeles.
Other details were not immediately released, and an after-hours call to Singleton's agent was not immediately returned.
Singleton, whose debut film, 1991's "Boyz N The Hood," earned him two Oscar nominations, has also directed "Poetic Justice," "Shaft," and "2 Fast 2 Furious." He was the producer of "Hustle & Flow," "Black Snake Moan" and the just-released "Illegal Tender."