A gunman opened fire at a small Christian university, killing at least seven people, wounding three more and setting off an intense, chaotic manhunt that ended with his capture at a nearby shopping centre, authorities in California said.

Police identified the suspect as 43-year-old One Goh, an Asian male.

The gunfire erupted around mid-morning on Monday at Oikos University. Heavily armed officers swarmed the school in a large industrial park near the Oakland airport and, for at least an hour, believed the gunman could still be inside.

Art Richards said he was driving by the university on his way to pick up a friend when he spotted a woman hiding in the bushes and pulled over. When he approached her, she said, "I'm shot" and showed him her arm.

"She had a piece of her arm hanging out," Mr Richards said, noting that she was wounded near the elbow.

As police arrived, Mr Richards said he heard 10 gunshots coming from inside the building.

The female victim told him that she saw the gunman shoot one person point-blank in the chest and one in the head.

Television footage showed bloodied victims on stretchers being loaded into ambulances.

Several bodies covered in sheets were laid out on a patch of grass at the school. One body could be seen being loaded into a van.

Police spokeswoman Cynthia Perkins said seven people were dead. She did not release any other details about the victims.