The official sent off Branislav Ivanovic and Fernando Torres during United's 3-2 win at Stamford Bridge, and the second decision in particular was heavily contested by the home players.
Chelsea did not go into details after the game, but a spokesman confirmed two separate incidents of Clattenburg's "inappropriate language" have been reported.
He said: "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.
"The match delegate will pass the complaint to the Football Association. We will make no further comment at this time."
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
Germany is one of the top teams ever and they will play the US on Sunday.
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Jamaica is in need of a win against the U.S. Get the jersey of the Reggae Boyz.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.