Authorities said the 43-year-old suspect is a Korean national who surrendered shortly after the shooting.
Witnesses say the suspect shot one of his victims at a reception desk at Oikos University before spraying bullets inside classrooms.
Student Deborah Lee said she heard the gunshots and fled.
"The first time when I heard it, I thought it was fireworks or just joking, but right after that one woman screamed a lot, shouting, and then my teacher went outside to check and then he said one woman told them, that somebody has a gun, run, and then we all of us in class just ran away," said Lee.
Oakland Police Chief Howard Jordan called the shooting "shocking and senseless" and described the scene as "extremely chaotic."
"There were several people hiding in locked buildings, locked doors, behind desks, as you can imagine very frightened, very scared. Some of them were injured, so we had to rescue them out. We had to force our way into a number of rooms," he said.
Oikos University founder, Pastor Jong Kim, tells the Oakland Tribune newspaper that the shooter is a former nursing student. Kim said he did not know whether the suspect was expelled from the school or dropped out.
The gunman's motive is also not known.
A spokesman for South Korea's foreign ministry said the government is monitoring reports about the incident, and called the shooting "unfortunate."