Part of the float — a truck and flatbed trailer with red, white and blue decorations that was loaded with hay bales — struck the child and knocked him to the ground, Hamm said. Edmond is just north of Oklahoma City.
"The driver, obviously unknowing what was going on, drove forward and ran over the child," Hamm said.
A number of people, including some children, witnessed the incident, he said.
"Many of the kids that saw it knew the child as well," Hamm said.
The boy was taken to an area hospital where he was pronounced dead. Police didn't immediately release his or his father's names. The father was not expected to face charges.
Hamm said the man wasn't reckless and didn't violate any traffic laws.
"It's just a freak, unfortunate accident," the officer said.
Police spokeswoman Jenny Monroe said investigators would wait until Friday to interview the father.
"We just haven't had a chance to speak with him and we're not going to do that today," Monroe said Thursday.
Thousands of spectators typically line the parade route in Edmond, where bands, floats, antique cars and marching groups pass by, according to the LibertyFest website. No one returned a phone call left Thursday for festival organizers.
The website says the festival hosts Oklahoma's largest hometown parade, with more than 100 entries.