Holmes said to his manager, Frank Lampard, that he was racially abused in the Derby dugout and reported the incident to the police.
The man was taken to a west London police station after being taken into custody at the ground and was later released on bail until an unspecified date in May.
Metropolitan Police told Sky Sports News that a file will be passed to the Crown Prosecution service for consideration.
The FA has not yet launched an investigation, but Sky Sports Newsunderstands the incident involving Holmes will feature in the referee’s report, which is usually released on a Monday.
A spokesperson for the Football Association said: “We encourage all fans and participants who believe that they have been the subject of, or witness to, discriminatory abuse to report this through the appropriate channels: The FA, our County FA network or via our partners at Kick It Out.”
Brentford confirmed the club would continue to work with the Metropolitan Police, promising the most severe sanctions for those convicted of discrimination.
“Brentford Football Club can confirm that a Season Ticket Holder was arrested following today’s game against Derby County,” said a club statement.
“The man in question has been accused of committing a racially-aggravated public order offence in the later stages of today’s game. He was identified at the time, removed from the ground and subsequently arrested.
“The club utterly condemns discrimination of any kind. It is abhorrent and has no place in society and we are determined to drive it out of Griffin Park.”
Derby manager Lampard mentioned the incident in his post-match interview, saying Holmes had complained of being racially abused, but said he was facing the pitch at the time and did not witness the incident.
Also on Saturday, Wigan Atheltic’s Nathan Byrne was subjected to alleged racial abuse on Twitter after scoring a late equaliser in a 2-2 draw with Bristol City at Ashton Gate.
Former QPR manager Chris Ramsey gave his view on the apparent rise in racist abuse in football, speaking to Sky Sports News at the British Ethnic Diversity Sports Awards on Saturday evening.
“We’re always disappointed, but it’s never really gone away has it?” said Ramsey. “Now there is more awareness, which is something I think is important.
“People are aware that these incidents are more prevalent than not.
“So, fair play to the people that are dealing with it and fair play to the people that have brought it to our attention.”