The pair have been cited for protesting with referee Andy D'Urso after he missed what they felt was handball in the build-up to the Robins' winning goal.
An FA statement said: "The charges relate to the pair's behaviour towards match officials at the end of Norwich's match against Bristol City on 29 March. Roeder and Clark have until 21 April to respond to the charge."
OUR REPORT ON SATURDAY:
Glenn"Roeder was not a happy bunny after the referee gave a decision against the Canaries in the final moments of the match at Bristol City on Saturday - and the hosts went on to score the winning goal.
Roeder confronted the referee in the centre circle at the end of the game, and followed him to the dressing room.
Roeder admitted after the game that he was "not proud" of his actions and that it was the fist time in his career that he had confronted an official in such a way.
FA spokesman: "It was reported and is now under consideration. We will be looking at the referee's report in conjunction with video footage, which we generally do when such things are reported."
Roeder: "I have never ever, in all my life, remonstrated with a referee straight after a game by walking on to the pitch.
"I am not pleased with myself, I am not pleased with myself at all, but that was how strong I felt about D'Urso's performance, particularly the incident that led to their winning goal."