Chaplin stated that the suspect then put his gun to his head and pulled the trigger.
Though the suspect was wearing a UPS uniform, investigators have yet to confirm he was actually an employee, Chaplin said.
UPS spokesman Steve Gaut said Wednesday that he believed the shooter "turned the gun on himself" but did not have additional information. Nor did Brent Andrew, spokesman for Zuckerberg San Francisco General Hospital, which had received the victims.
It was not immediately clear how many employees were at the building, but UPS said the warehouse employed 350 people.
When the police initially responded to the United Parcel Service facility in San Francisco, Chaplin said they did not know if the suspect was an actual employee there, or if was somebody dressed up like an employee, possibly committing an act of terror.
A San Francisco police officer gestures while standing outside a UPS package delivery warehouse where a shooting took place Wednesday, June 14, 2017, in San Francisco. At 11:47 a.m. the building was still on lockdown as police searched the building for other victims or workers hiding in place.
Three of those shot died of their injuries, while two others are being treated at the hospital.
San Francisco Assistant Police Chief Toney Chaplin says at a news conference that two others were wounded Wednesday.
"I was confused. They crossed the street and when they got to me, they said, 'Run, there is a shooter, ' so I started to run with them", she said.
She said they ducked as they boarded and told the driver to "go, go, go".
"The company is saddened and deeply concerned about affected employees, family members and the community we share", Gaut said.
In an unrelated event hours earlier, a gunman opened fire at a congressional baseball practice field in Alexandria, Virginia, injuring five people, including U.S. House Republican Whip Steve Scalise and two police officers.
Workers fled frantically into the streets shouting "Shooter!" and police swarmed in, authorities and witnesses said. This location is near a large UPS customer service center.
Witnesses say they heard several shots and saw people running out the UPS building.
Dozens of police cars, sheriff's cars and fire department vehicles were in the area, along with several ambulances.
Police sealed off streets in city's Potrero Hill area after the shooting. The shooter and all the victims were employees, UPS said in a statement.