As suspect Gene Atkins was firing rounds at police and officers were returning fire, Atkins and Corado were struck by gunfire, Moore said.
Corado was shot one time in the arm by one of two officers who were firing at Atkins. Moore described the bullet as going through Corado's body, and she eventually died at the scene.
Atkins, 28, was booked on suspicion of murder after an hourslong standoff with authorities at a Silver Lake Trader Joe's that left a woman dead as dozens of people remained barricaded inside the store.
Gene Evin Atkins remained in police custody at a local hospital the day after the shootout, Officer Drake Madison told KTLA. He was being held on $2 million bail.
Family identified the victim as Melyda Corado. She was the location's store manager, a law enforcement source said, according to the L.A. Times.
Albert Corado said his sister had worked at Trader Joe's for four to five years, CNN reported.
Atkins was allegedly armed when he hit a light post outside Trader Joe's and entered the store just after 3 p.m. on Saturday, according to officials. That happened after a pursuit that began about an hour and half before in South L.A., where he shot his grandmother and another woman, police said.
He had fled in his grandmother's vehicle with the other woman, police said, kidnapping her as he led police on a chase that ended in a crash just outside the Silver Lake supermarket.
Authorities surrounded the store that had some 40 to 50 people inside. Gunfire ensued and the suspect was struck once in the left arm, police said. No officers were injured.
After that, the suspect then entered the store, taking dozens hostage in a standoff lasting hours, police said. He negotiated with authorities until he requested that officers provide him handcuffs.
From inside the store, he handcuffed himself and then surrendered, according to police. Officers were seen escorting him out of the store around 6:30 p.m.
Los Angeles police later confirmed a female employee was fatally struck in the shootout and was pronounced dead at the scene.
Atkins' grandmother sustained seven gunshot wounds and underwent multiple surgeries, according to police. Her family later told KTLA she was expected to live and in stable condition.
Another woman, allegedly kidnapped by the suspect in his grandmother's Camry, was in stable condition after suffering a grazing gunshot wound to the head, officials said.
LAPD later said a 22-year-old woman was injured by broken glass at the scene of the shootout.
In addition to the suspect, five other people ages 12 to 81 were hospitalized, L.A. fire officials said. They were last listed in fair condition and police later said none of their injuries were life-threatening.