Campbell was handed a lifeline after referee Mark Halsey agreed to review the incident where the defender was seen to elbow Ole Gunnar Solskjaer as he tried to fend the player off with his arm.
Manager Arsene Wenger confirmed the move, saying: "We will appeal. I have seen it again on the video and it was obviously accidental.
"Sol didn't mean to hurt Solskjaer and his reaction did not help. A four-game ban would be very unjust."
The England star is currently facing a four-match ban following the red card in the titanic 2-2 draw with United, live on Sky Sports.
It rules Campbell out of crucial games in the run-in as well as the FA Cup final - and possibly England's friendly with Serbia and Montenegro - but the central defender claims that referee Halsey has already agreed to look at a video of the incident.
"I spoke to the referee after the game and he is willing to look at it," he said. "He was receptive to what I said. It looks bad with the naked eye because his head flings back.
But the video is not going to lie. It is going to show that it wasn't deliberate. Once it is not deliberate, that really helps me. That is going to be the point on which my season is defined.
"Hopefully, in his heart, he can make a decision that is the right one when he has seen the video and looked at all the different angles.
"I wasn't looking to injure him. I raised my arm, yes, but to protect the ball. It wasn't an elbow going into his face or anything like that. I was trying to palm him off and it was not like a clenched fist. My hand was open.
"You have to recognise the height difference as well. It is hard for me to accept because I have worked hard to get into this position and my season could be over."
