The player reported the comment to the match officials in line with Premier League protocols, Luton added.
"The matter was dealt with immediately by both Sheffield United and South Yorkshire Police, who are currently investigating," Luton said in a statement.
"We would like to thank both Sheffield United officials and the police for their swift actions in dealing with today's incident."
The Premier League condemned the incident in a post on social media.
"Racism has no place in our game or anywhere in society and we encourage anyone who hears or sees discrimination to report it so action can be taken," the league said on X.
"We will offer our full support to Carlton Morris and Luton Town FC, as well as continuing to work with clubs and authorities to ensure our stadiums are an inclusive and welcoming environment for all."
Jack Robinson and Anis Ben Slimane scored own goals in the final 13 minutes as Sheffield let a late lead slip and lost 3-2 to fellow strugglers Luton at Bramall Lane.
