The pair - who were reporting on terrorist attacks against foreigners in the kingdom - were shot by gunmen from a Jeep as they filmed the home of an al-Qaeda militant in the al-Suwaydi suburb of the Saudi capital Riyadh on Sunday (6 June).
Cameraman Simon Cumbers, 36, died at the scene while Gardner, 42, was rushed to hospital where he underwent surgery to gunshot wounds in his abdomen, leg and hand. As Broadcast went to press his condition was described as critical but stable.
A three-man BBC team was dispatched to Riyadh on Monday afternoon to assess the situation. BBC head of newsgathering Adrian Van Klaveren said the team - comprising head of high-risk security Paul Greeves, home news editor Jon Williams and world assignments editor Mark Perrow - would make arrangements for the care of Gardner and the return of Cumbers' body as well as looking into what happened.
"It is a very complicated situation," Van Klaveren said. "We want to know as much as we can about what happened. At the moment we know very little."
A report on the incident would be made on their return, he said.
Van Klaveren added that no BBC journalists were currently in Saudi Arabia and no further newsgathering trips were planned, although proposals to set up a permanent BBC base in Riyadh were still under consideration with the Saudi authorities.
In a move agreed before the Saudi attack, Van Klaveren said procedures had now been agreed to allow armed guards to protect BBC journalists in future dangerous situations. However, he added there were no plans to use them at present.