The gunman, who has not been identified, was wearing a uniform of the global parcel delivery service and shot himself in the head as police confronted him, San Francisco acting police chief Toney Chaplin told reporters.
Chaplin said the incident did not appear to terrorism-related.
UPS spokesman Steve Gaunt told local media that the shooter -- apparently a disgruntled employee -- burst into a room where workers were gathering for a morning meeting before heading out to make deliveries and opened fire.
The sprawling facility employs 350 people, UPS said in a statement.
"UPS confirms there was a shooting incident involving six employees within the company's facility in San Francisco earlier this morning," the statement said. "We understand that there are four deaths, although some individuals were transported to the hospital and we are unsure of their status at this time."
Police ordered residents and employees in the city's Portero Hill neighborhood and surrounding areas to shelter in place as they responded to the shooting.
Witnesses reported hearing multiple gunshots at the facility, which handles packages for delivery in the San Francisco area.
One woman whose husband was in the facility was quoted by local media as saying that the gunman shot his victims execution-style.
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