Police said the suspect, One Goh, 43, of Oakland, was arrested at Alameda's South Shore Center after the massacre at Oikos University, a small Christian school in Oakland, the Oakland Tribune reported.
One is a native of Korea and a naturalized U.S. citizen with no criminal record, who investigators think was acting alone, Oakland Police Chief Howard Jordan told reporters late Monday.
Gurpreet Sahota told the newspaper his sister-in-law, nursing student Dawinder Kaur, described the gunman -- said to be a former nursing student who hadn't been seen on campus for months -- as coming into a classroom, ordering everyone to get up against a wall, and drawing a gun before "people started running and he started shooting."
Sahota said Kaur was shot in the arm before running outside to call her brother.
Lisa Resler, 41, told the Tribune she was leaving an Alameda Safeway store when she saw a young Asian man wearing a beanie confronted by store security and then taken away by police. She said he appeared "very sedated" as he was handcuffed.
Police said the shooting started shortly before 10:30 a.m. PDT and sent panicked students running from the building. Some of the wounded were treated at the shooting scene and others were driven away in ambulances, the newspaper reported.
Five of the victims were pronounced dead at the scene and two died after being taken to a hospital, police said. None of the victims had been officially identified as of Monday evening.
Art Richards, of Oakland, who had arrived at the school around the time of the shooting to pick up a friend, told the Tribune a woman who came running from the building had said the gunman was a former student who had "seemed kind of weird, and that he wasn't all there and people would pick on him."
Pastor Jong Kim said One had previously been a nursing student at the university, but was no longer enrolled. Kim said he was unsure whether One had been expelled or dropped out voluntarily.
Kim said he heard about 30 shots fired.
"I stayed in my office," he said.
Oikos University is a small college specializing in nursing and religious studies, and caters to Korean students.
Oakland Mayor Jean Quan, speaking at a news conference late Monday, said, "We'll have to question the availability of guns and the need for other services in our community."
Plans call for a memorial service for victims Tuesday evening at the Berkeley Korean United Methodist Church, the Tribune said.