Chelsea have alleged that a "large group" of Manchester United supporters made homophobic chants at Monday's Premier League match.
The Blues said people making "unacceptable" chants were either prevented from entering Stamford Bridge or ejected during the game.
"This behaviour will not be tolerated," said Chelsea on Tuesday.
"Those supporters will be banned from attending matches at Stamford Bridge in future."
Chelsea added that they have "passed on the details of those supporters" to Manchester United so they can "take appropriate action".
"Chelsea is a diverse and inclusive club and will always take firm action against all forms of discriminatory behaviour," they added.
In a statement, United responded: "Manchester United has a long-standing commitment to equality, diversity and inclusion.
"Our fans were vocal as always in their support for the team and we appreciate that loyal backing. However, this song directed against Chelsea FC - or any other club - by some of our fans runs counter to our values.
"We will continue to engage in campaigns to raise awareness and fight discrimination in all forms."
United won the match 2-0 through goals from Anthony Martial and Harry Maguire.