The shooting happened Saturday while the boy was in the car with his grandmother and his 1-year-old sibling, Lt. Steven McClanahan of the Little Rock Police Department said.
When the grandmother, identified by police as 47-year-old Kim King-Macon of Little Rock, stopped at an intersection, a man in the car behind her honked, the police said.
King-Macon honked back, and the suspect got out of his car and fired a gun, police said.
The grandmother at that point had not realized the 3-year-old was shot and drove away, police said. She then pulled over and realized the boy was injured and called police.
Acen was taken to Arkansas Children's Hospital where he died, police said. His sibling was not injured.
Police called it a road rage incident and said the grandmother was innocent and had no relationship with the suspect.
McClanahan, who called the shooting "tragic," said police have interviewed King-Macon and believe she is telling the truth.
No arrests have been made, McClanahan said today, adding that police have received tips and are actively pursuing leads.
Local and federal authorities have offered a combined $40,000 reward for information leading to the arrest and conviction of the suspect.
ABC News' David Caplan and Angie Yack contributed to this report.