Coroner's officials identified the man as 18-year-old Jeovany Mendoza of Van Nuys.
Police responded to a 911 call at about 8:30 p.m. Saturday near Saticoy Street and Tobias Avenue. Once on the scene, officers found Mendoza holding the knife to the woman's throat.
After Mendoza refused to drop the weapon, police say one of the officers opened fire, killing him. According to investigators, the woman may have suffered cuts to her hands and throat, but was expected to be OK. Her identity was not immediately released.
No one else was seriously injured.
The circumstances surrounding the initial threat were not immediately known. The case remains under investigation.
City News Service contributed to this report.