He suffered the injury when a teammate landed on the back of his leg during the scrimmage, and Miles classified the injury as minor.
"Fournette got a slight sprain and is in a boot and so we're getting some of the healing going," Miles said. "I don't know [when he'll be back] at this point, but I know it's not ... In his words, he'll be fine."
Fournette, who is ranked No. 3 in ESPN's preseason Heisman Watch after breaking single-season school records with 1,953 rushing yards and 22 touchdowns last season, tops Todd McShay's list of top running back prospects for the 2017 NFL Draft.
Derrius Guice will move up to first-team running back while Fournette's recovers. Guice rushed for 445 yards and three touchdowns as a freshman last season, playing in all 12 games.
LSU has already been hit hard with preseason injuries. Defensive end Christian LaCouture was lost for the season after tearing his ACL tear and linebacker Corey Thompson will miss at least another month with a leg injury.
"Sometimes the odds don't play in your favor," Miles said.
Fournette, a junior, made headlines last week after a video showing him "slap boxing" with a teammatewent viral.
LSU opens the season against Wisconsin on Sept. 3 at Lambeau Field in Green Bay, Wisconsin.