Vladimir Nekrasov's lawyers had requested that their client be released on 49-million ruble ($2 million) bail, the sum that Russian tax authorities say he owes in back taxes for January 2005 - December 2006.
The 47-year-old businessman was detained on January 23 alongside Semion Mogilevich, 61, a Ukrainian-born Russian passport-holder accused by both Russian authorities and the FBI of involvement in criminal activities. The arrest of the two men has been described as a major police operation, involving elite commandoes.
Tax evasion charges were brought against the pair on January 30.
"The charges were brought after auditors estimated that Arbat Prestige was worth $1.5-2 million," Alexander Dobrovinsky, one of Nekrasov's lawyers, said.
"It is a tasty morsel that somebody wants to appropriate," he added.
The lawyer added that Nekrasov had received an offer around a week ago to sell the company. He declined to give any further details, however.
The Moscow City court will consider on February 18 a similar appeal for bail by Mogilevich, also known as Sergei Shnaider. He is charged with being behind a tax evasion scheme allegedly utilized by Arbat Prestige.
Arbat Prestige is one of Russia's leading cosmetic retailers. Established in 1989, it opened its first retail outlet in 1998, and currently runs a network of 64 outlets across Russia. The company reported income of around $346 million in 2006.