Shnaider, 62, also known as Semyon Mogilevich, was detained in Moscow in late January alongside the owner of the Arbat Prestige cosmetics chain Vladimir Nekrasov.
"My client suffered extremely high blood pressure and a heart attack last Saturday. We are requesting that his custodial supervision be changed as we believe he is unable to receive the necessary medical treatment in custody," Alexander Pogonchenkov said.
In April, the Moscow City Court refused to release Shnaider, who complained about his health, on $2 million bail, the amount of the back tax claimed against Arbat Prestige. The court ruled that the suspect should remain in custody until June 23 as the investigation was continuing.
Shnaider, who is known under a number of different names, has been wanted by a number of countries, including the United States, for more than 15 years for involvement in organized crime and fraud. Believed to control the largest Russian mafia syndicate in the world, he is suspected of being involved in arms dealing, drug trafficking, prostitution and money laundering.
He served two jail terms in the Soviet Union in the 1970s - for currency dealing offenses and fraud.
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.
