Police said the man from Aintree, Merseyside, was arrested on suspicion of a racially aggravated public order offence. He is in custody and being interviewed by detectives.
Friday's match at Anfield was stopped briefly while 20-year-old midfielder Adeyemi, on loan at the League One club from Premier League Norwich City, alerted the referee.
On Saturday, Liverpool issued a statement on their website saying:
"Liverpool Football Club continue to work closely with Merseyside Police to establish all the facts surrounding the incident that occurred during last night's game.
"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."
The incident occurred after Liverpool forward Luis Suarez was handed an eight-game ban by the FA for racially abusing Manchester United defender Patrice Evra in October.
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