Duncan, known for his Academy Award and Golden Globe-nominated role in "The Green Mile," was 54 when he died. Doctors said he never fully recovered from the heart attack.
A family friend was taking flowers to Duncan's grave when she came upon his headstone, which was spray-painted with racist graffiti.
Police are now investigating the vandalism as a hate crime, according to the Chicago Defender.
A picture of a cartoon black face was attached to the center of his headstone -- an offensive black stereotype known as a Sambo figure.
The family notified the cemetery, which removed the figure immediately. The Los Angeles Police Department determined that the defacement could be considered a hate crime and has begun an investigation.