Chelsea confirmed that they had lodged a formal complaint to the Premier League over two comments Clattenburg allegedly made towards two of Roberto Di Matteo's players.
"We have lodged a complaint to the Premier League match delegate with regards to inappropriate language used by the referee and directed at two of our players in two separate incidents in today's match," a club spokesman said.
"The match delegate will pass the complaint to the Football Association. We will make no further comment at this time."
Clattenburg has vowed to co-operate with any investigation.
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. No further comment will be made until this matter has been properly investigated."
All four officials - the referee, his two assistants and the fourth official - wear microphones and ear pieces that allow them to hear what each other is saying throughout the match. What is said between them is not recorded.
The revelation that Chelsea had made the complaint rounded off a dramatic day which saw the Blues lose their unbeaten top-flight record after Javier Hernandez struck the winning goal 15 minutes from time.
The goal sparked wild celebrations among the United players, with Hernandez and Rio Ferdinand - who had been booed throughout the game - gesturing gleefully towards a pocket of the home support in the Matthew Harding Stand. The home fans reacted by hurling abuse and surging towards the front of the stand. Chelsea said they were also looking into reports that missiles were thrown after a steward was injured.
Source: PA
Source: PA