Riyadh, Saudi Arabia: A teacher killed two staff at a private school owned by a prominent Saudi billionaire in Riyadh on Wednesday, a security source told AFP.

The school was closed and no children were there at the time, the US embassy in Riyadh said.

Police were hunting a suspect of Iraqi origin who worked at the school, the security source said, after the rare shooting.

"A teacher took a gun and then he went to the school room and he killed the assistant school principal and one of the employees," said the source who asked not to be identified because a formal statement would come later from Riyadh police.

Investigators are treating the case as a criminal matter and "not a terrorist incident," the source said.

Saudi media spoke of "disagreements" between the suspect and victims.

"There has been a shooting at Kingdom School in Riyadh," the US embassy said on its Twitter account.

"School (is) closed, no children present. Please avoid area," the Twitter post said, without elaborating on casualties or motives behind the shooting.

By late afternoon an AFP photographer observed only one police car entering the school grounds, which were quiet.

Most schools in Saudi Arabia are on holiday.

Nobody answered the school's main phone line, and mobile numbers listed in the school handbook were either off or unanswered.

Kingdom School is part of a group owned by Prince Alwaleed bin Talal, chairman of Kingdom Holding Co whose diversified investments include Citigroup and Time Warner.

The school, which has several campuses, opened in 2000 and offers boys' and girls' education from kindergarten to high school, according to its website.

The school has both a Saudi curriculum and an international programme leading to an American diploma.

Kingdom Holding says on its website that the schools group has more than 4,000 students and 300 teachers at various locations in Riyadh.

Since 2014 the Islamic State group has claimed bombings and shootings that killed dozens in Saudi Arabia, targeting minority Shiites and members of the security forces.

But criminal shootings with multiple victims are unusual.

In February last year a teacher reportedly killed six people at an education department office in the southern region of Jazan.