The boy was being dropped off at the Red Cedar Elementary School parking lot at the end of the parade route when he was fatally injured, police said.
Investigators are still talking to witnesses to figure out exactly what happened, Bluffton Police Chief Chris Chapmond said in a statement.
“Our thoughts and prayers go out to the family of Ameer and to those who witnessed the accident. This is an accident that can only be described as tragic and unimaginable,” Chapmond said.
An autopsy is planned for Tuesday, authorities said.
Counselors were available Monday throughout the Beaufort County School District where Ameer was an elementary school student, district spokesman Jim Foster said.
The annual Christmas parade started about 10 a.m. Saturday and ended in Bluffton Park.