The U.S. military plans to build a base on the island as part of a so-called Asian pivot -- to move 60 percent of its naval assets to the Pacific by the end of the decade.
The "Wall Street" and "Platoon" director has been involved in protests against the move, The Hollywood Reporter said Saturday.
"Ever since the Second World War, the [United States] has been building military alliances and setting up military bases overseas," Stone told the Hankyoreh daily. "A lot of those bases are in Japan and Korea. Jeju Island is less than 310 miles from Shanghai. It could end up on the front lines if a military conflict breaks out between the [United States] and China."
Pamphlets protesting the plans were handed out at the Busan International Film Festival in South Korean. The pamphlets feature Stone carrying a sign that said "peace" during a demonstration in Gangjeong village on Jeju Island.