The dramatic development, which came after a stormy top of the table clash at Stamford Bridge on Sunday, will add fire to Wednesday evening when the two sides meet again in London in the League Cup.
"We have lodged a complaint to the Premier League match delegate with regard to inappropriate language used by the referee and directed at two of our players in two separate incidents during today's match," said a Chelsea statement.
"The match delegate will pass the complaint to the football association. We will make no further comment at this time."
Sky Sports News claimed late Sunday that one of the players involved was Chelsea's Nigerian star John Obi Mikel.
It was reported by the Daily Telegraph on Monday that Mikel accused Clattenburg of directing a comment of a racial nature at him.
Professional Game Match Officials (PGMO), the body which represents Premier League referees, released a statement which read: "PGMO is aware of the allegations and they are being treated with the utmost seriousness.
"Mark will co-operate fully and welcomes the opportunity for the facts to be established."
All four officials -- the referee, his two assistants and the fourth official -- wore microphones and ear pieces that allowed them to hear what each other was saying throughout the match.
But under FIFA guidelines, what is said between them is not recorded.
The complaint came after a highly-charged encounter in which Clattenburg dismissed two Chelsea players before Javier Hernandez secured the points for United with a goal that Chelsea manager Roberto Di Matteo insisted should have been ruled out for offside.
Goals from Spaniard Juan Mata and Brazilian Ramires had earlier hauled Chelsea back in the game after an own-goal from defender David Luiz and a Robin van Persie strike had put them 2-0 down early on.
Branislav Ivanovic and Fernando Torres were sent off but it was the decision of Clattenburg to issue Torres a second yellow card for diving after a challenge by Jonny Evans that was the focus of much of Di Matteo's frustration.
The Spanish international had been booked for an earlier challenge on Tom Cleverley before his 68th minute clash with Evans.
"He played the ball between his legs, then he gets kicked on his shin and goes down -- it's as simple as that," said Di Matteo. "It's a free-kick for us and might even be a sending off for Evans as he is through to the goal. I was shocked. I thought it was going to be a free-kick for us and a foul for us, not against us.
"And the decisive goal was an off-side goal. It's a shame that game like this has to be decided in that manner by officials.
"I have spoken to the referee. Surely when he's going to watch the images he's going to realise that he made big mistakes."
United manager Alex Ferguson viewed things differently.
"Did Torres intend to dive? He could have gone on and he didn't," he said.
"I thought he went down. I think Jonny may have just caught him a little bit but you can carry on running and he chose to go down.
"He could have carried on and scored. That is what I can't understand. I would never have missed that chance to go through. I would never go down, but he's gone down and that is the issue. And he's been booked, so it's his own fault.
"It's 10 years since we won here and there have been some shocking decisions down here. It's very difficult to come here and get all the decisions, I must say that."
Having seen his side lose back-to-back games -- Chelsea were beaten by Shakhtar Donetsk in the Champions League last week -- Di Matteo will be anxious to recover quickly and avoid the risk of a repeat of the dip in form the club suffered at this stage of the two previous seasons.
"Today, we looked like a team that wanted to win this game and we were very strong out on the pitch to show that," he said.
"Obviously decisions went against us and made it very difficult but in the long run, this is a team that has a lot of qualities, even though we might find moments like this, we know that we can come out of it, once we get everybody back. We are a good team."