Gardner, 42, who is a leading expert on Al Qaeda and works full-time reporting on the war on terror, is being treated in hospital in Riyadh.
Irishman Cumbers was a freelance journalist and cameraman who has worked throughout the world filming international news stories for the BBC as well as Associated Press Television and ITN.
The two men had travelled to Saudi Arabia last week following the latest terrorist attacks in the country at Khobar, which saw Islamic militants kill 22 foreign workers, including one British man. Three of the gunmen who took part in the carnage were able to slip through the Saudi security net and make their escape.
Richard Sambrook, BBC director of news, said: "Our thoughts are with the families of Simon and Frank tonight. We are in touch with them and offering them all the support that we can. We are seeking more details about what happened in this incident."
According to BBC reports, Riyadh's police chief said the attack was carried out by "unknown elements" on Sunday afternoon.
The latest attack took place in the al-Suwaydi neighbourhood, which has been the scene of a number of recent anti-terror raids.
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