Prokhorov, 42, who ranks fifth on Forbes' list of Russian billionaires, with wealth estimated at $13.5 billion, was arrested while on holiday at the resort in the French Alps for allegedly supplying prostitutes to his wealthy friends.
In a communique Prokhorov released to French media, the billionaire said: "In January, my winter vacation in France was spoiled by local police, who arrested me and my friends without giving any reasonable explanations. The investigation has since not moved an inch forward."
Prokhorov was arrested along with several young Russian women during a police raid on January 9. The suspects were transferred to Lyons and later released without charges. The raid was part of a months-long police operation to expose a prostitution ring.
A Courchevel regular, Prokhorov was known for throwing lavish parties every time he visited the resort, inviting dozens of prostitutes. Fellow Russian visitors said after his detention that French police may have suspected him of involvement in pimping activities.
"Neither I nor my friends intend to come to France until the investigation is completed and apologies are made," the businessman said in the statement, which was also posted on his internet blog.
"I have questions, which have so far had no answers. Why did French authorities engage a great number of experts and equipment in this obscure case using taxpayers' money? Why did they arrest a lot of people and keep them in custody without clear grounds? Why was the investigation not completed although the arrests and questioning did not yield any evidence that would allow charges to be brought?"
The tycoon's lawyer said on Wednesday that the probe should be closed as soon as possible, and that French law-enforcers' actions were unacceptable.
"Mikhail Prokhorov's defense team has so far taken a fairly quiet position," Alexander Genko-Starosselsky said. "We considered that a mistake could have been made in the very beginning and that French authorities would close the case in line with legal procedures."
"But clearly, we could drastically alter our position if no decision follows within a reasonable period of time," he said.