Schneider acquired the Davidoff shop from Zino Davidoff for $930,000 in 1970, and the two built Davidoff into a global empire. Where as it was once only a cigar shop and a cigar brand, the name now appears on a variety of luxury products, including fragrances.
Riccardo Gullotti, a member of the Oettinger Imex board, will succeed Schneider as chairman. Day-to-day operations of the group are handled by chief executive officer Reto Cina.
Schneider, who said in a statement that he stepped down "in order to unburden" himself, will remain a member of the board.