Kerimov was arrested at Nice airport overnight into Tuesday.
Forbes Magazine ranks Kerimov as Russia's 21st richest businessman with a fortune of United States dollars 6.6 billion.
But state news agency RIA Novosti reported that Mr Kerimov had entered France on his private passport and often only diplomatic couriers and embassy and consulate employees enjoy diplomatic immunity under an worldwide agreement.
Image A villa owned by Mr Kerimov in Cap d'Antibe in southeastern France
Suleiman Kerimov, a senator in the Federation Council, the upper chamber of the Russian parliament, who has an estimated fortune of €5.3 billion, is being questioned in connection with the alleged laundering of funds amassed in a tax fraud.
But after losing a significant part of his fortune, he sold most of his shares in the club. His family controls Polyus, Russia's largest gold producer.
Kerimov was once a member of the ultra-nationalist party Liberal Democratic Party, which he left in 2007 to join the ruling United Russia party.
Mr Kerimov did not include any property in southern France on his asset declaration as a senator this year and his representative has denied that he owned properties there.
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