The incident occurred about 3:30 p.m. near Los Angeles County+USC Medical Center when the man broke free from a detective and two officers who were escorting him to the hospital, said Los Angeles Police Detective Meghan Aguilar.
The man ran away and confronted a woman in an SUV and forced her to get out. The officers who were pursuing the man eventually caught up to him and one officer shot the suspect at the intersection of Zonal Avenue and Cummings Street, Aguilar said.
The man was transported to a hospital in stable condition and no officers were injured during the incident, she said.
The stolen SUV remained at the scene and appeared to have front-end damage from a crash.
She added that the investigation is ongoing and what exactly led to the shooting is still being determined.
No weapon has been found at the scene, but the vehicle and the surrounding area had not been searched.
The man was being taken to the hospital for a follow-up examination from an incident that occurred Tuesday in the 5200 block of Ithaca Avenue in El Sereno.
Police responded to that incident about 4:30 p.m. and found the same suspect had a knife to a woman's throat at the doorway of an apartment, Aguilar said. Officers shut down and surrounding the area when the woman ran out of the apartment. After negotiating with the man, he eventually surrendered without incident, the detective said.
The woman was not injured during the incident.