Kerimov, 51, spent a second night on Tuesday at a police station in the southern resort city, where he was arrested on arrival at the airport on Monday night.
He can be held for up to 48 hours before either being brought before an investigating magistrate to face charges or released.
One of his lawyers confirmed that he was still in custody but refused to comment on the investigation.
A source close to the probe told French news agency AFP that he was suspected of laundering "tens of millions of euros" hidden away from tax authorities.
Kerimov, who is listed by Forbes magazine as Russia's 21st richest person with an estimated net worth of 5.4 billion euros, is a frequent visitor to the Côte d'Azur.
In 2006, he crashed his Ferrari while speeding along Nice's seafront, sustaining severe burns.
He made his fortune during the privatisations that followed the break-up of the Soviet Union, owning stakes at various times in energy, banking and mining giants, such as Gazprom, Sberbank and potash producer Uralkali.
He also owns Russia's Anzhi Makhachkala football club.