Prosecutors had asked for Kerimov to be detained as they continue their investigation.
The court rejected that call but set the bail high, a wise move given that Kerimov is a billionaire.
He left the court, surrounded by his own bodyguards, without making any comment.
Born in Dagestan, Kerimov represents the Caucasus republic in the Russian Federation Council and his arrest at Nice airport last month provoked an angry response from President Vladimir Putin's government.
At the time he was ordered to post five million euros' bail, had to surrender his Russian passport and was ordered not to leave the Alpes-Maritime region.
Five luxurious villas
Kerimov is suspected of laundering money and dodging millions of euros in taxes when he bought five villas on the Cap d'Antibes under somebody else's name.
A large part of the payments is believed to have been made in cash, sometimes coming from Switzerland or Monaco, while a lower price was declared to the authorities.
Nice public prosecutor Jean-Michel Prêtre on Monday put the money concealed by the operations at 500-750 million euros.
Four out of the five villas have been seized, the other having been resold.
A total of 13 people have been charged in the course of the investigation, which started in 2014.
One of them, estate agent Irina Sadikova, was released from detention on Wednesday on the payment of 300,000 euros' bail.
She has admitted receiving a commission of two million euros, which she hid in Switzerland, for the sale of one of the villas.
Kerimov employee Cédric Faugeroux was ordered to pay 800,000 euros in bail.
Oligarchs on the Riviera
Kerimov is far from the only wealthy Russian to have invested on the French Riviera, where advertisements in Cyrillic lettering can be seen in and around luxury hotels and other hangouts of the rich.
Nor is he the only one to attract the judicial authorities' attention.
The Russian authorities themselves alerted the French to one such case 10 years ago and a court on Monday confirmed the only conviction in that case, estate agent Jean-Louis Bordes.
He lost his appeal against a one-year suspended sentence, a 100,000-euro fine, a 500,000-euro fine for his company, Sifi, and the confiscation of a ch teau at Antibes.
Declaring the sentence "disproportionate", he said he would appeal to the European Court of Human Rights.
Bordes was found guilty of helping oligarch Boris Berezovsky, who died in 2013 under suspicious circumstances, to buy the ch teau for 8.4 million euros in 1996, as well as a neighbouring property purchased the following year.
Berezovsky bought yet another villa for 11.5 million euros in 2001 along with land worth 1.3 million euros.
The money used in the purchases appears to have been laundered through a complex network of companies around the world.
Berezovsky was one of the first Russians to make a fortune after the collapse of the Soviet Union and was close to president Boris Yeltsin.
However, he fell out with Putin and fled to London.
He was subsequently sentenced in his absence to seven years' jail in Russia for abuse of influence and embezzling money from the national airline, Aeroflot.FrenchcourtfreesRussianoligarchmillioneuros'bail