The employee who died was Martin Haro-Lozano, 45, of Orland, California, Johnston said.
Officials did not identify the shooter, but Johnston said he has a history with the Red Bluff workplace.
The shooting victims were taken to St. Elizabeth Community Hospital in Red Bluff, spokeswoman Allison Hendrickson told The Associated Press. She confirmed that four were hospitalized, but declined to provide more details.
Some of the 200 workers inside the facility locked themselves in a room , employees told KHSL-TV.
The suspect was shot in the chest about 3:45 p.m., dispatchers told the newspaper.
Scott Thammakhanty, an employee at the facility’s receiving center, told the Redding Record-Searchlight that he heard the shooter fire from the rifle.
“It went on and on — I don’t even know how many times he fired,” Thammakhanty said. “I just know it was a lot.”
Thammakhanty and others started running for their lives, and he saw people lying on the ground as he went, he said.
Fellow employee Franklin Lister told the New York Times he had just started work when a coworker ran down the hallway shouting: “Active gunfire! Active shooter!”
Vince Krick told the Record-Searchlight that his wife and son work at the facility and he was on his way to pick up his wife when he saw the flames. Neither was hurt, but his wife told him not to come to the front entrance, the newspaper reported.
“It was real crazy, because, you know, you can’t do nothing,” Krick said.
Dispatchers told the Record-Searchlight that at least one woman had been shot. A man had also reported his leg being run over when the shooter rammed a vehicle into the building, but the man wasn’t sure if he had been shot, dispatchers said.
Walmart spokesman Scott Pope told the Record-Searchlight that the company was “aware of the situation” and working with law enforcement.
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