The shooting happened around 8:30 a.m. at the Classic Tobacco smoke shop in the 10900 block of Firestone Boulevard, according to the Los Angeles County Sheriff's Department.
Four male suspects entered the store and tried to rob the owner at gunpoint, sheriff's Lt. Daniel Vizcarra told reporters.
"The store owner produced a handgun, fired and struck one of the individuals who then collapsed on scene," Vizcarra said.
The suspect who was struck by gunfire was taken to the hospital, where he later died. The shop owner was not injured.
Authorities searched a nearby neighborhood for the other suspects who fled. A sheriff's SWAT team surrounded a home and took two suspects into custody in the area of Elmcroft Avenue and Hermes Street.
One suspect remains on the loose.