The 73-year-old man accelerated his SUV into the Gulf Shores High School band in the city of Gulf Shores, a beach resort 30 miles west of Pensacola, Florida, city spokesman Grant Brown told reporters at a news conference.
"A teenage band has just started to march down the parade route when they were struck from behind," he said.
The authorities said they do not believe the incident was intentional.
"Every indication is that it was a tragic accident by an elderly man," Gulf Shores Police Chief Ed Delmore told the press briefing.
There was no indication drugs or alcohol were involved, Brown said.
City officials investigating the incident have canceled the parade and closed part of a highway and several roads.