The incident happened around 10:30 p.m. Sunday near 11th Street East and Avenue R, according to the Los Angeles County Sheriff's Department.
Investigators said the suspect asked the victim if he could enter her apartment because someone was chasing him. When the woman refused, he forced himself into the residence.
That's when the suspect attempted to assault the victim with a hammer, officials said. The victim then ran into her room, where she retrieved her firearm in efforts to protect herself.
"The suspect overpowered the victim and took her firearm away from her and subsequently shot her," said Deputy Jose Lainez.
Before the shooting, neighbors said they were screaming at the man, telling him not to pull the trigger and to let the woman go, but he shot her anyway.
"Once he shot her, he dragged her out the house and that's how she got downstairs," said one resident who only identified herself as Destiny. "Once she got downstairs, she was able to get away from him."
Destiny said it appears that before the woman was shot, she quickly moved her head, resulting in a flesh wound instead of a more serious gunshot injury to her head.
"God was on her side," Destiny said. The woman was taken to the hospital and was listed in stable condition.
After shooting the woman, the suspect took the victim's child, described as being between 10 and 12 years old, hostage. When authorities arrived on scene, they found the suspect holding a gun to the child's head.
Deputies were able to talk the suspect into letting go of the child, who was not physically hurt.
Residents of the apartment complex told Eyewitness News they've seen the suspect several times and he appears to be an ex-boyfriend. However, authorities said multiple times that the suspect was a stranger.
The suspect, who was not identified, remains in custody and was booked on suspicion of attempted murder, assault with a deadly weapon and kidnapping. Authorities described him as a convicted felon with an extended criminal history.