The development comes after Brown's comments in a post-match interview at Dens Park on Sunday.
Brown was critical of referee Alan Muir, who awarded Aberdeen a penalty which they scored to earn a 1-1 draw and relegate Dundee from the top flight.
Aberdeen midfielder Peter Pawlett has since been offered a two-match suspension for simulation in winning the spot-kick.
An SFA statement explained Brown was being cited for: "Making comments in a media interview that criticise a decision and the performance of the match officials in such a way as to indicate incompetence."
The Dark Blues boss has already claimed he will quit if he is punished by the SFA for his comments.