The statement, released via the club's official Twitter page, informs supporters that the board have made a decision to not have fans present at the game.
"According to the decision taken by our board, our supporters will not attend AS Monaco-Besiktas game," the statement read.
"We're kindly asking you not to go to Louis II Stadium in order to prevent the risk of ban."
The decision comes as a reaction to events in April when kick-off in the Europa League quarter-final first-leg tie against Lyon was pushed back 45 minutes due to crowd trouble involving Besiktas supporters.
Projectiles and fireworks were launched on to the field and around 500 police were stationed at Parc Olympique Lyonnais.
Besiktas were punished by UEFA as a result with a two-year, suspended exclusion from any European competition, meaning any further incidents would put the Black Eagles' participation in the Champions League in serious jeopardy.
The Turkish champions sit top of Group G with six points from their opening two games. Last year's semi-finalists Monaco are yet to register a win in this season's competition having been thrashed 3-0 at home to Porto following a 1-1 draw with RB Leipzig.