Simon Cumbers, a freelancer working for the BBC, was killed in the Suwaidi district of the capital on Sunday.
The wounded man was identified as the BBC’s security correspondent, Frank Gardner.
“Two British nationals were shot by unknown elements in a working-class district of Riyadh at 17:40 (1440 GMT) on Sunday. One was killed and the other wounded,” the Saudi Press Agency (SPA) reported.
A statement from the British embassy in Riyadh said Gardner was in a serious but stable condition after undergoing surgery.
Suwaidi is a slum area where security forces have arrested many suspected armed dissidents in a crackdown in recent months.
Cumbers and Gardner were filming the house of a man wanted by the Saudi authorities for alleged links to al-Qaida.
Both had been in Saudi Arabia since last week’s attack on a foreign residents’ compound in the eastern city of Khobar in which more than 20 people were killed by armed dissidents.
The attack helped push world oil prices to record highs before producers pledged to raise output.
Gardner is the BBC’s expert on al-Qaida and has produced highly critical news items on the group since the 11 September 2001 attacks on the US.
Saudi Arabia, the world’s largest oil exporter, has been fighting an insurgency supported by Saudi-born Usama bin Ladin’s al-Qaida network for over a year.
Foreign Minister Prince Saud al-Faisal said on Sunday that anti-government forces were going after soft, random targets.
He called on foreign governments to hand over Saudi dissidents abroad with alleged links to the violence that has rocked the kingdom.
Fifty people were killed in Riyadh last year in a string of bombings. Security forces have killed or arrested at least eight on a list of 26 wanted dissidents.