The man, from Aintree, is being questioned by officers from Merseyside Police who are investigating the incident which took place in the second half of the match at Anfield on Friday night.
Late in the FA Cup third-round fixture, Tom Adeyemi, on loan from Norwich, appeared to take offence at something shouted from the Kop.
There then appeared to be discussion between the fourth official and a police officer down by the tunnel while the match was continuing.
A police spokesman said: "Merseyside Police can confirm that tonight a 20-year-old man from the Aintree area of Merseyside has been arrested on suspicion of a racially aggravated public order offence following an incident at Anfield on Friday evening.
"The man is currently in custody being interviewed by detectives."