The Cook County Medical Examiner has identified the woman as Ann Sconza.
Sconza was walking in the road in the 3800-block of South Pulaski, which is near an exit ramp for the Stevenson Expressway, when she was struck.
The car then fled the scene.
Police say they are looking for a white, older-model Pontiac or Buick with a damaged windshield.
Sconza, believed to be in her 40s, was pronounced dead at 10:40 p.m. Friday at Mount Sinai Hospital, according to a spokesman for the Cook County Medical Examiner's office.
Police said she suffered massive head trauma, and a Saturday autopsy determined she died of multiple injuries from an auto striking a pedestrian. The death was ruled an accident.
Sconza was possibly homeless and asking motorists for money, police said.
The Sun-Times Media Wire contribued to this report.