A total of 10 people were hit, five of whom were pronounced dead at the scene. Two others died later in hospital. Other people were found hiding in classrooms at the small Christian college, he said.
The gunman was arrested about 8km away near a Safeway supermarket in Alameda County, according to local media. CNN reported that he told the store's customer services counter that he had just shot a number of people.
"He actually commandeered a victim's car, and drove it to Alameda, and that's where he surrendered,'' added Jordan, describing the college as a "very bloody scene''.
The San Francisco Chronicle cited a woman injured in the attack as saying a student who had always "looked crazy'' stood up in a class at the Christian college and started shooting.
"A gunman came into the college and fired multiple shots,'' an Oakland police spokeswoman said. "We do have fatalities. I cannot confirm the number of fatalities we have at this time.''
Lisa Resler, 41, said she was leaving the Alameda store with her daughter when she saw a young Asian man wearing a hat being confronted by store security. She described him as looking "very sedated'' as he was handcuffed.
Within minutes of the mid-morning shooting, SWAT teams took position around the building, some smashing glass with sledgehammers and rushing inside as officers helped students evacuate the campus, the Chronicle reported.
Angie Johnson, 52, said she saw a young woman leaving the building with blood coming from her arm and crying, "I've been shot, I've been shot.''
The woman said the shooter was a man in her nursing class who rose up and shot one person at point blank range in the chest before he started spraying the room with bullets, Johnson said, cited by the Chronicle.
"She said he looked crazy all the time,'' Johnson said the victim told her. "But they never knew how far he would go.''
The victim "had a hole in her right arm the size of a silver dollar with blood coming down,'' she added.
Five ambulances were dispatched to a "multi-patient medical scene,'' the Oakland Fire Department said on its Twitter feed, while police described the suspect as "male, Asian, heavy build, khaki clothing.''
The school says on its website that it strives to "provide highest standard education with Christian value and inspiration.''
"Oikos University has a very specific goal and mission to offer education programs in the area of religious studies, music, and vocational nursing,'' it said.
"We motivate, educate and equip students in such a way that they will be able to live an enriched life by fulfilling their goals in life and serve the community with their learned professions and skills,'' it added.
- AP, AFP