The Russian government summoned France's deputy ambassador after Kerimov was detained upon arrival at the airport in the French Riviera resort of Nice on Monday night.
A source close to the probe told AFP that Kerimov was accused of hiding tens of millions of euros from tax authorities while buying a string of properties on the glitzy Riviera through intermediaries.
His detention prompted angry Russian MPs to pass a resolution branding the arrest a violation of the 1961 Vienna Convention on Diplomatic Relations, urging Moscow to press for his release.
“The senator status and the fact that he is a Russian citizen is a guarantee that we will, of course, put in all possible efforts to defend his lawful interests,” Kremlin spokesman Dmitry Peskov said.
He stressed that 51-year-old Kerimov holds a diplomatic passport, though he is not believed to have used it when he flew in to Nice on personal business Monday.
France's foreign ministry said Kerimov enjoys immunity from prosecution “only for actions carried out in the exercise of his functions”.
Suleyman Kerimov. Photo: AFP
It will be “up to the judge hearing the case to decide” whether or not the allegations relate to his official role and are covered by immunity, a ministry spokesman said.
Listed by Forbes magazine as Russia's 21st richest person with an estimated net worth of $6.3 billion (5.4 billion euros), Kerimov made his fortune during the privatisations that followed the break-up of the Soviet Union.
A regular visitor to France's Cote d'Azur, he has owned stakes at various times in Russian energy, banking and mining giants such as Gazprom, Sberbank and potash producer Uralkali.
One of his lawyers confirmed to AFP that Kerimov was still in custody, but refused to comment on the investigation.
He can be held for up to 48 hours in France before either being brought before an investigating magistrate to face charges or released.
A tax lawyer and two Swiss businessmen have already been charged over the case.
Journalists in front of the police station where Kerimov is being questioned by investigators. Photo: AFP
In September, local newspaper Nice-Matin reported that a villa on the Cap d'Antibes peninsula near Nice, valued at 150 million euros and thought to be owned by Kerimov, had been seized as part of an investigation.
Swiss financier Alexandre Studhalter — one of the three men charged — appealed the decision, denying he was a frontman for Kerimov, who is originally from Russia's North Caucasus region of Dagestan.
The billionaire previously controlled the region's Anzhi Makhachkala football club, which at one point topped the Russian league when he poured millions into buying players like Roberto Carlos and Samuel Eto'o.
But after losing a significant part of his fortune, he sold most of his shares in the club.
His family now controls Russia's largest gold producer, Polyus.
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.
Since 2008, he has represented Dagestan as a senator in the Federation Council, the upper house of Russia's parliament.
In 2006, he crashed his Ferrari while speeding along Nice's seafront, sustaining severe burns.