The punishment centres around an incident in the Premier League encounter at Carrow Road on October 26, with Norwich midfielder Leroy Fer having kicked the ball in the net after it had been put out of play for Alex Tettey to receive treatment.
A large group of players were involved in a subsequent scuffle as referee Mike Jones disallowed the goal, with Norwich fined the same amount on Tuesday.
The FA explained on Wednesday that Cardiff's punishment was decided later than Norwich's because the Welsh club had rejected the standard penalty.
In a statement, the organisation said: "Following an Independent Regulatory Commission hearing, Cardiff City have been fined £20,000 for failing to ensure their players conducted themselves in an orderly fashion.
"Cardiff admitted the charge, but rejected the standard penalty of £20,000. However, following a non-personal hearing the standard penalty was applied."
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