The French champions salvaged a 2-2 draw in the Group B match at the Veltins-Arena courtesy of Souleymane Camara's 90th-minute leveller, which Girard appeared to celebrate by raising his middle finger in the direction of Schalke boss Huub Stevens and his team's dugout.
The two coaches were then seen having a heated exchange of words after the final whistle.
Stevens is quoted by AFP as saying after the match that Girard was "calling for a yellow card after every foul and that's not fair."
Both managers were coy when answering questions about the incident after the game, although Stevens did voice his frustration at letting a team with 10 men hold his side to a draw at home.
"Of course we are upset," the 68-year-old said. "They have two shots on goal and both of them go in. We needed to clinch this game earlier.
"Even against 10 men we should know that at Champions League level you need to make the most of your chances."
A UEFA disciplinary panel will consider the charge when it meets on Tuesday October 9, when it will also look at Montpellier fans who let off fireworks at the ground in Gelsenkirchen.