Santa Ana police identified the woman on Wednesday as 27-year-old Alma Ramirez of Santa Ana. Officials released a booking photo from a separate incident.
Shortly before 8 p.m. Tuesday, police were called to the area of 5th and Mountain View streets after receiving a report about a woman who had attempted to stab a man with a knife.
While officers were en route, authorities said Ramirez tried to carjack an elderly couple. During that incident, Ramirez stabbed the owner of the car, authorities said.
Police said when they arrived on scene, Ramirez fled on a bicycle with a knife in her hand.
Officers followed her to the 3300 block of West 5th Street, where authorities said Ramirez began waving the knife around. That's when an officer-involved shooting took place.
Ramirez was transported to an area hospital in critical condition. She is expected to survive.
Police said Ramirez will be arrested on several charges, including carjacking and assault with a deadly weapon.