Chelsea midfielder Claude Makelele became involved and this was followed by a number of other players on both sides becoming embroiled in a scuffle.
Rovers admitted the charges but Chelsea pleaded not guilty and were fined £15,000.
The FA also warned both clubs as to their future conduct.
Rovers Handed Ten Grand Fine For Chelsea Fracas
The incident in question occurred when Rovers striker Morten Gamst Pedersen challenged Chelsea goalkeeper Petr Cech and players from both sides became involved in a scuffle during the game between the two sides at Ewood Park last month, which Chelsea won 1-0.