Los Angeles police said it happened in the 6600 block of Topanga Canyon Boulevard, which is the address of the Westfield Topanga Mall, just before 12:30 p.m.
According to LAPD, the woman was walking with her 2-year-old child in a stroller in a parking lot near a restaurant.
The investigation appeared to be centered outside the Cheesecake Factory. Police tape closed off part of the parking lot, aerial video from AIR7 shows.
The suspect, who police identified as 29-year-old Shayne Suffern, approached the victim and said. "Give me back my baby."
That's when police say Suffern opened his backpack, pulled out an AR-15 rifle and attempted to fire at the victim. The rifle malfunctioned, and as the victim attempted to flee, she grabbed her child from the stroller.
LAPD said Suffern then stabbed the woman in the back of her right shoulder with a knife. The child was not harmed.
The woman then reportedly ran inside the restaurant screaming and covered in blood.
Officers found Suffern in a nearby parking lot and took him into custody. LAPD said the victim sustained a 3-inch stab wound and was taken to the hospital in stable condition.
Footage from AIR7 showed police searching a dark Mercedes sedan near an Office Depot store.
Suffern was arrested on suspicion of attempted murder. His bail was set at $5.325 million.
The investigation is ongoing, but police said there is no evidence to suggest the suspect and victim know each other. Previously, officials said it began as a child custody issue.
Anyone with information regarding this incident is urged to contact Topanga Area Detective Acevedo at 818-374-4820.