The complaint deals with words specifically used against John Obi Mikel but the Blues decided not to pursue an allegation referee Clattenburg also used words understood to have been interpreted as racist towards Juan Mata during Sunday's game following an internal investigation carried out by external legal counsel.
Chelsea said in a statement: "Chelsea Football Club today lodged a formal complaint with The Football Association regarding inappropriate language directed at John Mikel Obi by referee Mark Clattenburg.
"This is a result of a thorough investigation carried out by the club, and led by outside legal counsel, of all information available to us including interviews with a number of players and staff.
"Following Sunday's Premier League game against Manchester United, club board members were quickly made aware, upon entering the home dressing room after the final whistle, that there were allegations of inappropriate language directed at Chelsea FC players by Mr Clattenburg during the game.
"Board members began establishing the details of the allegations, speaking to all relevant players and staff. After those initial interviews, it was clear that the matter had to be reported.
"The correct protocol for doing so was to report the incidents to the match delegate, and the club took immediate steps to inform him as soon as he was available. It was not a decision the club took lightly.
"Since reporting the matter to the delegate, the club and outside legal counsel have conducted further investigations.
"Having completed that process, we have now followed the correct protocol and lodged a formal complaint with The FA regarding John Mikel Obi.
"There was not sufficient evidence to support a second claim to the FA with regard to the alleged verbal abuse of another first-team player."
The matter is already the subject of FA and police investigations and Chelsea's statement added: "We will cooperate fully with the FA and the police as they each investigate the matter.
"As events on Sunday are now subject to those investigations, we are unable to comment further until those processes are complete."
The FA refused to comment on tonight's development as they continued their probe, while the Metropolitan Police were not immediately available for comment.
Press Association Sport understands Clattenburg categorically denies any wrongdoing.
He and his fellow referees were said yesterday to have been shocked an angered by the claims.
The 37-year-old had already vowed to co-operate with any inquiry.
The officials' in-game conversations are not recorded but the extraordinary fallout from the weekend's events have led to calls for that to change.
Press Association Sport understands referees could be canvassed to establish whether they would be in favour of such a move, which would require the approval of the International Football Association Board, in the same way as goalline technology has.
Police became embroiled in their second high-profile racism case in 12 months following a complaint from the Society of Black Lawyers, whose chairman has vowed to continue escalating such allegations from the world of football until the FA increase the severity of their own sanctions.
The FA could announce such changes when they report back to the Government on the all-game response to February's Downing Street summit on discrimination in football.
The Professional Footballers' Association have already announced a six-point plan to tackle the problem, which includes a proposal of guaranteed sackings for racist abuse.