The Federal Security Service said TNK-BP's Ilya Zaslavsky and his brother, Alexander, had been detained for allegedly passing along secret oil and gas information, the Novosti news agency said.
The brothers are members of the British Council alumni club.
Police subsequently raided both the central office of TNK-BP and the Moscow office of Britain's BP.
The Zaslasvsky brothers, who both have U.S. and Russian citizenships, belonged to the club, which was set up for foreign graduates of British universities. Alexander Zaslavsky was identified as a leading figure with the club.
The British Council voiced its concern over the arrests, prompting Russian officials to declare there was no connection with the arrests.
The council's regional offices in Russia were closed earlier this year over alleged tax violations.

