Police also shot and killed the suspect at the Burlington shop in the North Hollywood area of San Fernando Valley, police said.

The girl was identified by the Los Angeles County coroner as Valentina Orellana-Peralta.

A man had been acting erratically and threatening to throw items from the upper floor, witnesses told KCBS-TV.

They said he also attacked a woman with a bicycle lock while the shop was crowded with holiday shoppers.

Officers were called to a report of an assault and others of shots being fired, police said.

Investigators did not find a gun at the scene.

Officers shot and killed the suspect at the store but one of the bullets went through a drywall behind the man and hit the girl.

Officers found her dead after seeing a hole in "a solid wall that you can't see behind", said Los Angeles Police Department assistant chief Dominic Choi.

Investigators did not know whether she was in the dressing room before the violence started or whether she ran inside to hide, he added.

"This chaotic incident resulting in the death of an innocent child is tragic and devastating for everyone involved," police chief Michel Moore said in a statement.

"I am profoundly sorry for the loss of this young girl's life and I know there are no words that can relieve the unimaginable pain for the family."

Mr Moore promised a "thorough, complete and transparent investigation" into the shooting and said a critical incident video including 911 calls, body camera and other video footage will be released by Monday.

Local news reports showed a woman who appeared to be the assault victim with a bloodied face being placed in an ambulance.

The victim was taken to hospital with moderate to serious injuries, Fire Department spokesperson Nicholas Prange said. Mr Choi said she had wounds to her head, arms and face.

The suspect's name has not been released and the woman who was attacked is not being identified.

Investigators are trying to determine whether the assault was random or targeted.

Mr Choi said they do not believe the teenager was related to the person who was attacked.