The suspect had been shot in the chest by about 3.45 p.m., dispatchers told the newspaper.
Scott Thammakhanty, an employee at the facility's receiving centre, said he heard the shooter fire from a semi-automatic weapon.
"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.
Thammakhanty told the newspaper that he didn't know his identity.
Fellow employee, Franklin Lister, 51, told the New York Times he had just started work when a coworker ran down the hallway shouting: "Active gunfire! Active shooter!"
Dispatchers told the Record-Searchlight that at least one woman had been shot. A man had also reported his leg getting run over when the shooter rammed a vehicle into the store, but the man wasn't sure whether he'd been shot, dispatchers said.
Walmart spokesman Scott Pope told the Record-Searchlight that the company is "aware of the situation" and working with law enforcement.
"We don't have any additional information to share at this time," Pope said.
- AP