Chris Mortensen and Adam Schefter of ESPN reported Coughlin also needed stitches on his head and was hospitalized overnight.
Coughlin said another rider came "out of nowhere" and clipped the front of his bike. Doctors said his recovery will take four to six weeks.
Coughlin went 170-150 in 20 seasons as an NFL head coach with the Jacksonville Jaguars and New York Giants from 1995-2015, winning two Super Bowls with the Giants. He returned to Jacksonville as an executive from 2017 to 2019, when he was fired amid accusations of mistreatment of players.
He has not been hired by an NFL organization since his departure from Jacksonville.