The FA have also charged Hull City manager Steve Bruce with misconduct for his post-match comments regarding Tottenham Hotspur's controversial 80th-minute penalty in Sunday's 1-0 defeat.
"It was a joke decision. I shouldn't say this and I might get fined, but would we have got it? I am not so sure," Bruce said at the time of the decision to award the spot kick."
Leroy Fer's disallowed goal for Norwich City in stoppage time sparked the scuffle at Carrow Road.
The clubs are being charged "for failing to ensure their players conducted themselves in an orderly fashion. It follows an incident which occurred in or around the 94th minute of their fixture on Saturday," the FA said in a statement on Thursday.
Fer kicked the ball into an empty net from a throw-in after Cardiff keeper David Marshall had put it out of play for injured Norwich midfielder Alex Tettey to receive attention.
That prompted an angry response from the Cardiff players.
Bruce and both clubs have until 1800 GMT on November 4 to respond to the respective charges.
Championship (second tier) sides Blackpool and Blackburn Rovers were also charged by the FA for failing to control their players following an incident near the end of their 2-2 draw on Saturday.
(Reporting by Mike Collett; Editing by Alison Wildey)
