The shooting was reported shortly before midnight near the intersection of Mesa and First streets, according to the Los Angeles Police Department.
The two victims were transported to Harbor-UCLA Medical Center in Torrance, where the critically injured woman underwent surgery, an LAPD spokesperson said. The boy, whose injuries were not life-threatening, was listed in stable condition.
The female victim is 19 years old, authorities said. The boy was described only as a juvenile.
Police described the suspect being sought in connection with the shooting as a 13- or 14-year-old girl. No other details were available.
Investigators say there was an argument between the suspect and the female victim. The shooter pulled out a small handgun and fired multiple shots, hitting both victims.
The suspect fled the scene on foot.
The circumstances that led to the shooting were under investigation.