The incident happened shortly before 9 p.m. Sunday on the 1400 block of South La Cienega Boulevard near Alcott Street at Smoke 'N' Gifts.
Police originally said that the two people who were shot by the shop owner were trying to rob the store. But authorities now say one of them, who remains hospitalized in critical condition, was a customer, not a thief.
The other person was trying to rob the store. He was taken to the hospital, where he later died. Police are still searching for his accomplice.