UEFA has opened a disciplinary case against the Croatian Football Association after a fan ran on the pitch following Luka Modric's goal in the 1-0 win against Turkey.
UEFA says Croatia is charged with "field invasions by supporters," with the case to be judged by their disciplinary on July 21.
Croatia and Turkey have also been charged with fans lighting fireworks, and Turkey for a firework being thrown.
National associations are held responsible by UEFA for their fans' behaviour in and around stadiums.
After Modric's 41st-minute goal at the Parc des Princes on Sunday, a man came to the edge of the field from the main stand.
Wearing a red-and-white Croatia shirt, he huddled with blue-shirted players by the corner flag before being led away by stadium security staff.
The incident happened in the first Euro 2016 game after Russian fans charged at England supporters at Stade Velodrome in Marseille on Saturday evening.
UEFA is set to announce punishments for Russia's football federation on Tuesday.