The three reporters were working in the southern city of Astrakhan when they were "assaulted by unidentified men in a coordinated attack," BBC said in a statement.
"Our staff were badly beaten, their camera destroyed and then taken," the statement said.
BBC spokesman James Hardy added separately: "All are OK."
"The cameraman is continuing to receive treatment for concussion and other injuries," he added in written remarks.
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They later "discovered that recording equipment - which was in their vehicle, at the police station - had been electronically wiped".
The incident is "clearly part of a coordinated attempt to stop accredited news journalists reporting a legitimate news story," the BBC said, calling for a thorough probe.
Astrakhan police spokesman Pyotr Rusanov told Russian news agencies that authorities had launched an inquiry into a robbery and were looking for assailants.
Russia has enforced a virtual blackout on any information concerning the deployment of regular troops to Ukraine.
Rights campaigners have said at least 200 Russian servicemen might have died in eastern Ukraine where fighting between pro-Russia separatists and Kiev forces has claimed nearly 2,900 lives since April.
Several journalists covering the story have been attacked or harassed in recent weeks.
Last month Lev Shlosberg, a local opposition lawmaker and journalist in the western city of Pskov was hospitalised with head and eye injuries after an attack by three unidentified men.
Shlosberg was one of the first people to report on the deployment of local paratroopers to Ukraine.
His newspaper Pskovskaya Guberniya said that dozens of Pskov-based soldiers had been killed.