On the basis of Hankook’s share price at the close of trading on Monday, the stake is worth 729.4 billion won (474 million euros, $653 million dollars).
Michelin said it would dispose of the shares via a private placement with institutional investors through US bank Citigroup and that the process would begin immediately.
Hankook is the biggest tyre maker in South Korea.
The two firms have been linked since 2003 by a cooperation agreement under which Michelin was to increase its holding to 10.0 percent, a level almost reached in 2008.
Michelin has a strategy for developing in emerging markets, and notably in China, India and in Brazil where it has increased its production capacity.