"It is with great sadness that I report the loss of my longtime friend and client," his agent, whose name wasn't reported, said. "James was the biggest East Asian U.S. star the country had known. ... The world has lost another wonderful actor, sadly I lost a dear friend."
Shigeta was perhaps best known in the United States for his role as executive Joseph Takagi, who is shot in the head by a character played by Alan Rickman in 1988's Die Hard.
His 50-year career included roles in WWII flick Midway and 2009's The People I've Slept With.
He won a Golden Globe for promising newcomer in 1960 for his role in The Crimson Kimono.