The brawl occurred after Gorka Pintado saw red for a challenge on Robbie Savage on Saturday with the Swans leading 1-0.
Players from both sides piled in after Pintado was subsequently shoved to the floor and the actions have seen both sides charged with failing to control their players with Derby having until March 9 to appeal and the Swans until March 5.
Derby player James McEveley has also been charged with improper conduct after he was sent off earlier in the second half.
