The shooting occurred outside a home in the 6300 block of South Hoover Street, near West Gage Avenue, according to the Los Angeles Police Department.
Officers responded shortly before 5:30 a.m. to a report of a grand theft auto in progress, the LAPD said. They arrived to find the suspect, a man in his 30s, inside the victim's vehicle in the driveway.
The officers saw that the suspect was armed with a gun, authorities said, and police opened fire. The man "was struck by gunfire and taken into custody," the LAPD said on Twitter.
Los Angeles Fire Department paramedics responded and pronounced the suspect dead at the scene. His identity was not immediately released.
"The suspect's gun remained at scene and will be booked as evidence," the LAPD said in a tweet.
No officers or bystanders were injured.