Off-duty police officer fatally shoots man at California Costco

The man's two family members were also critically injured.

One person was killed and two others critically injured after an off-duty police officer opened fire inside a southern California Costco Friday night, police said.

The shooting took place after an argument and was not an active shooter situation, a Corona Police spokesperson told reporters at a press conference.

The police officer was assaulted "without provocation" while he was holding his young child by a 32-year-old man at the store, according to police. The off-duty officer pulled out a gun and opened fire, striking the individual -- who the officer did not know -- and two members of the suspect's family.

The man who was fatally shot was identified as Kenneth French, from Riverside, California. Two of his family members are in critical condition, according to police. Police did not release further details about the ages or genders of those injured.

At 7:46 p.m. local time Friday, Corona police officers arrived at the Costco Wholesale club in Corona, which is about 50 miles outside of Los Angeles.

"Upon entering Costco, officers located four injured people on the floor. One subject succumbed to their injuries at the scene and three other subjects, including an off duty officer from another agency, were transported to local hospitals in unknown conditions," Tobias Kouroubacalis, public information officer for the Corona Police, wrote in a statement to ABC News soon after the incident.

The Los Angeles Police Department (LAPD) confirmed that one of its Southwest Division patrol officers fired his gun and was also injured while at the Costco off-duty. He is not detained or under arrest.

"Our officer suffered minor injuries in the incident and was transported to a local hospital where he was treated and released," the LAPD said in a statement. "The Department has initiated an Administrative Investigation and is working with the Corona Police Department to learn more about the incident."

No one else fired a weapon in the incident, police said, "contrary to earlier reports."

ABC News' Alex Stone contributed to this report.