Todd Heap, 37, was moving the vehicle in his driveway in the city of Mesa on Friday afternoon when the tragedy occurred.
The girl – the youngest of five children – was rushed to a local hospital, but did not survive her injuries, Mesa Police said.
Police said there were no suspicious circumstances and that Mr Heap showed no signs of impairment, though their investigation is still underway.
The former tight end attended Arizona State University and was a first-round draft pick in 2001 for the Baltimore Ravens.
He played with the team for 10 seasons and became the Ravens’ all-time leader in touchdown catches.
He later played two seasons for the Arizona Cardinals, before retiring in 2013.
In September 2014, Mr Heap was inducted into the Baltimore Ravens Ring of Honour, which honours former players and personnel who have made outstanding contributions to the organisation.
Prayers up for Todd Heap and his family. Couldn't imagine the pain he and his family is feeling right now.— Damon Harrison (@BigDame900) April 15, 2017
Tributes have been pouring in on social media from fellow football players and fans.
“Prayers up for Todd Heap and his family. Couldn’t imagine the pain he and his family is feeling right now,” American football defensive tackle for the New York Giants Damon Paul Harrison wrote on Twitter.
Former placekicker Jay Feely said: “My heart is broken for Todd Heap and his family. One of the kindest persons I’ve ever met and a man who lives for his family.
My heart is broken for Todd Heap and his family. One of the kindest persons I've ever met and a man who lives for his family. 🙏🏻🙏🏻— Jay Feely (@jayfeely) April 15, 2017
The retired footballer has raised money for sick and disadvantaged children through his own charitable foundation, the Todd Heap Family Paediatric Centre, which he opened in Baltimore in 2010.