Star strikers Tresor Kandol and Jermaine Beckford were sent off in the 1-1 draw at Priestfield and then the Whites boss was sent to the stands himself by McDermid, who Wise claimed swore at him after the match.
An FA statement said: "The charge relates to Wise's conduct towards referee Danny McDermid at half-time during the game against Gillingham on Saturday. The FA can confirm that it has received a complaint from Leeds United regarding the conduct of the referee towards Wise after the conclusion of the game. This is now under consideration."