Fans of the Spanish club displayed a "Flick Heil" sign, echoing the Nazis' "Sieg Heil", in reference to their club's German coach Hansi Flick as they played at Monaco on September 19.
"FC Barcelona reject any type of justification for violence," the club said in a statement, adding it "will both comply with and apply this sanction".
"The club is set to strengthen current measures and adopt suitable further initiatives to prevent future occurrences and apply sanctions to those responsible," the statement added.
Barcelona's next away game is at Serbian club Crvena Zvezda in Belgrade on November 6. They lost the game at Monaco 2-1.
September 27, 2024