Born in Honolulu, Shigeta studied acting at New York University. He later joined the Marines and entertained troops during the Korean War. Before beginning his acting career, Shigeta was a singing star in Japan. He made his film debut in 1959's The Crimson Kimono, and the following year won the Golden Globe for Most Promising Newcomer, along with George Hamilton, Tony Donahue and Barry Koe.
In 1961, Shigeta starred as Wang Ta in the film adaptation of the Broadway musical Flower Drum Song. In Die Hard, he played executive Joseph Takagi, who's killed by Alan Rickman's Hans Gruber. He also starred in the 1976 World War II film Midway.