The 52-year-old founder of TCS, which co-owns Russia's leading online bank Tinkoff, said in March he was battling acute leukaemia, a day after the U.S. Department of Justice said it was charging him with filing false tax returns.
He has not commented on the charges, which could see him facing up to six years in prison if he is extradited to the United States and convicted.
TCS said in a statement the Rigi Trust connected to the Tinkov family had sold 10,655,737 global depositary receipts (GDR) at $30.50 each, or around 5.3% of TCS total shares, via an accelerated bookbuild secondary placement.
The Tinkov family planned to use up to $200 million to launch a charity fund "to support people suffering from any kind of blood cancers," Tinkov said in his separate statement on Friday.
He added that he also planned to use "some of the cash to deal with personal legal challenges," without providing details.
The Tinkovs would continue to own around 35% of the group following the placement, with some 58% of TCS remaining in free float, and would not cut their stake further for at least six months, Tinkov's statement said.
TCS's GDRs were down 5% at 1035 GMT to $31.25 apiece. "The stock will be under pressure today, but we still like TCS Group's investment case," Aton brokerage said in a note.
Tinkov tried to sell his business to Russia's top internet company Yandex in a $5.5 billion cash-and-share deal this year but the talks fell apart in October.
(Reporting by Tatiana Voronova and Katya Golubkova; Editing by Andrew Heavens)