Boutte was assessed a personal foul late in the Tigers' 16-14 loss to Wisconsin for his hit on defensive back D'Cota Dixon following a game-sealing interception. Boutte was immediately tossed from the game for the hit.
Boutte will miss LSU's first home game against Jacksonville State on Saturday as a result.
"Josh made a mistake and will serve a one-game suspension because of it," Miles said. "Even though this was done by mistake, a play like this does not belong in the game of football and therefore action must be taken.
"This play does not define Josh as a person and is not indicative of the type of player he is. We sincerely apologize for his mistake."
Miles initially defended his player in the immediate aftermath of the play but said he had to see the tape before assessing any punishment.
Miles noted that Boutte called Dixon on Monday morning in order to offer an apology for the hit.