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According to CNN, two other people were also shot and survived.
Police responded to a report of an active shooter around 8:55 am local time at the UPS San Francisco Customer Centre -- package sorting and delivery facility that employs about 850 people.
Officers arrived to learn the suspect was still inside the building, Chaplin said.
A police "contact team" soon found him armed with an assault pistol, the assistant chief said.
"The suspect put the gun to his head and immediately discharged the weapon," he said.
Though the suspect was wearing a UPS uniform, investigators have yet to confirm he was actually an employee, Chaplin said.
Local media quoted witnesses within the warehouse at the time of the incident as saying that the gunman went in through the front entrance and started shooting, without saying anything -- once at the back of a victim and then at the heads of some others.
Employees of UPS were evacuated from the facility as officers tried to search for additional victims and witnesses, Xinhua reported.
For a moment, appealing that "don't put officers at risk," San Francisco Police Department posted a message on its Twitter social media network account calling for media to "stop showing video and photos of (police) Tactical Units search the roof and other parts of the scene."
There have been no words on possible motives of the shooter or what led to the workplace shooting.
UPS said in a statement that pending the police investigation, it "cannot provide information as to the identity of persons involved at this time" and that regarding those injured, it is "unsure of their status at this time.