Several British newspapers last week printed a picture taken during Chelsea's dramatic 5-4 League Cup win over Manchester United at Stamford Bridge on Wednesday which appeared to show a fan making a monkey gesture at striker Danny Welbeck.
"Officers investigating a complaint regarding alleged racist behaviour at Stamford Bridge on Wednesday, 31 October have arrested a man," London's Metropolitan Police said in a statement.
"The 28-year-old man was arrested... after attending a west London police station by appointment.
"He was arrested on suspicion of a racially aggravated Section 4A Public Order Act offence and currently remains in custody at the west London police station."
Enquiries are continuing, it said.
Chelsea said last Thursday that they were holding their own separate investigation into the incident and appealed for anyone who could identify the fan to contact the club.
The incident comes after Chelsea confirmed they had complained to the Football Association about "inappropriate language" used by referee Mark Clattenburg towards midfielder Jon Obi Mikel during an English Premier League defeat by Manchester United on October 28.