Shnaider, also known as Semyon Mogilevich, is a Ukrainian-born Russian passport-holder wanted by both Russian authorities and the FBI for involvement in organized crime and fraud.
Shnaider's defense had asked the court to release him on 50 million ruble ($2 mln) bail, which is the amount of back tax claims against Arbat Prestige, but the court refused, ruling that he remain in custody until June 23.
The president of the Russian leading cosmetic retailer Vladimir Nekrasov, 47, and Semyon Mogilevich, 61, were arrested on January 23 and charged with tax evasion.
Russian authorities allege that he was behind a tax evasion scheme said to have been used by Arbat Prestige.
Arbat Prestige was established in 1989 and opened its first retail outlet in 1998. It currently runs a network of 64 outlets across Russia. The company reported income of around $346 million in 2006.