The deadly incident happened around 9 p.m. Tuesday while the store on San Vicente Boulevard was still open, according to the Los Angeles Police Department.
Police say the victim was involved in an argument with another man, who appeared to be a transient, when that suspect stabbed the victim multiple times before leaving the scene.
The unidentified victim later died at the hospital.
People in the area say they witnessed a similar argument earlier in the evening, but are unsure if the two incidents were related.
"They were right in front of this retail store here... I couldn't really make out what they were arguing about, I kept my head down and was walking, but it was definitely getting contentious," said Arash Naghdi, who works in the area.
The investigation into the stabbing is ongoing. Additional details about the suspect were not available.