Oldham were facing Liverpool in the third round of the FA Cup.
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, the 20-year-old, on loan from Norwich, appeared to take offence at something shouted from the Kop.
Despite reassurance from his team-mates and Liverpool players Dirk Kuyt and Steven Gerrard, the right-back seemed close to tears.
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."
Liverpool, who won the match 5-1, said they are also investigating the incident.
The club issued a statement saying it was continuing to work closely with the police to establish the facts surrounding the incident.
The statement said: "We take this matter extremely seriously and have today provided the police with the evidence we currently have available to us.
"This includes CCTV coverage and still photography of what we believe to be the relevant part of the stadium, statements from matchday stewards in that area and full access to all the footage captured by the cameras filming the match for our in-house TV operation.
"In addition, we have examined records of the tickets purchased in that part of the ground to see if they provide any additional information and have passed that on to the police.
"Finally, we would also urge any of our supporters who witnessed this incident or saw the individual involved and who have not already done so, to contact either the club or the police."
The investigation takes place as Liverpool striker Luis Suarez is currently seeing out an eight-match ban for racially abusing Manchester United defender Patrice Evra.