The behaviour of some home supporters delayed Saturday's Sky Bet Championship fixture at The Den, which the Rams won 5-1, for several minutes in the second half.
Objects were thrown at Derby full-back Adam Smith, a player the Lions had on loan last season, as he went to take a throw-in with the score at 3-0.
Millwall fans spilled down to the front of the stand by Smith and referee Keith Stroud had to move the players away as stewards attempted to restore calm.
Meanwhile, over on the other side of the stadium, a supporter went into Derby's technical area in front of the dugout and appeared to push Rams manager Nigel Clough before racing off across the pitch and disappearing into the crowd.
Clough then substituted on-loan Tottenham right-back Smith to help defuse the situation.
Asked if Derby will make an official complaint, Clough told reporters ahead of his side's trip to Bolton on Tuesday night: "We will just see what happens this week with the referee's report and with the Football League. I don't think it is up to us to do anything at all.
"Personally, I was not scared but you do worry for the players' safety when a supporter gets on the pitch.
"It is not good to see such scenes but it is not our problem. It is something for Millwall and the authorities to deal with."
The FA told the Press Association on Monday morning that it will wait until it has all the information available before deciding its next step.