AIR7 HD was over the scene around 11:10 p.m. as several law enforcement vehicles gathered in the area of Arcadia and Spring streets. The incident also prompted a response from SWAT.
The hostage and the police officers were unharmed in the confrontation, according to the Los Angeles Police Department.
A nearby homeless encampment appeared to be the focus of the search for the suspected shooter, and police said the suspect was isolated to a tent in the encampment before being shot.
The woman was taken into custody and hospitalized in unknown condition shortly before midnight. She was not immediately identified.
The California Highway Patrol shut down nearby freeway off-ramps, and the southbound 101 Freeway at the 110 was also closed due to the incident.