The shooting occurred June 16 inside an apartment building in the 1000 block of Long Beach Boulevard, near 10th Street, police said.
A security guard told officers a woman had pointed a gun at his head, robbed him of his keys and said she was going to kill him, according to the LBPD.
The video shows the officers confronting the woman, instructing her to put her hands up. She pointed a firearm -- later identified as a replica -- through a crack in the door, resulting in the shooting, police said.
The woman then barricaded herself in her apartment.
"SWAT responded to the scene and attempted to deescalate the situation. After about four hours of unsuccessful attempts to contact her, SWAT officers deployed gas," police said.
The woman eventually surrendered and was taken into custody.
Police said she sustained a gunshot wound to her upper body and was taken to a hospital with injuries that were not life-threatening.
Detectives recovered the replica firearm from the scene, and no officers or bystanders were injured, police said.
"As with all officer-involved shooting incidents, the department will be conducting a full and thorough multi-level review of the incident," police said in a statement. "The Los Angeles County District Attorney's Office will conduct an independent investigation of the incident, as they do with all officer-involved shootings that result in injury or death."