The incident happened Friday evening at a home on West 52nd Street, just east of Broadway.
The Los Angeles Police Department says a woman was holding her own son hostage with a knife during what was supposed to be a custody exchange.
At one point, police say, the woman stabbed the boy - believed to be around 11 - in the neck. That's when officers opened fire, wounding the woman.
The boy and woman were both rushed to a local trauma center for treatment.