US TV footage showed wounded people emerging from buildings at Oikos University in the city of Oakland.
Policemen have surrounded the buildings, but it is not clear whether there is still a suspect on the scene.
Oikos University is a religious institution offering courses in theology, music and nursing, according to its website.
The Associated Press news agency is quoting law enforcement sources as saying five people are dead.
Johnna Watson, of Oakland Police, said: “We know this to be a Korean college. A gunman came in to the college and fired multiple shots.
“We do have fatalities, I cannot confirm the number of fatalities we have at this time. We additionally have victims who have suffered from gunshot wounds.”
Johnna Watson added that medical services as well as police were at the scene.
The Oakland Fire Department says it was first notified of the shooting at about 10:50 local time .
One witness, Brian Snow, told local news station KGO-TV: “One of the people who was inside the building, she was saying there is a crazy guy inside.
“She did say someone got shot in the chest right next to her before she got taken off in an ambulance.”
A police officer at the scene told reporters the gunman had not been identified.
Reports described the suspect as a Korean man in his 40s, with heavy build and wearing khaki clothes.
The US House Ethics Committee has voted to release its report on former Republican Representative…
ABC News has agreed to pay $15 million to President-elect Donald Trump to settle a…
South Korea’s parliament has voted to impeach President Yoon Suk Yeol over his failed attempt…
Israeli war planes have carried out more than 100 air strikes in Syria on December…
President-elect Donald Trump has threatened to impose 100% tariffs on the BRICS countries if they…
Syrian troops have withdrawn from the city of Aleppo following an offensive by rebels opposed…