The Football Association announced the charges on Tuesday but no charges have been issued against any individuals, though that could change if new evidence comes to light.
Nottingham Forest boss Billy Davies has accused Derby manager Nigel Clough of kneeing him in the back of the leg during the scuffle.
The FA said in a statement: "The FA has charged both Derby County and Nottingham Forest with failing to control their players following events at Pride Park on Saturday 30 January.
"The charges relate to a mass confrontation between players and officials from both clubs in the latter stages of the fixture. All parties have until 17 February to respond to the charges."
It is the second time this season that the clubs have been charged over a mass melee.
Earlier this season both sides were fined following a skirmish, Forest £25,000 and Derby £20,000, with £10,000 each of the fines suspended.
It now looks certain that both sides will have to pay the £10,000 as well as extra possible sanctions.
Source: Team Talk