An investigation into the incident, which happened during Saturday's clash between Swansea and Norwich, will continue.
A 23-year-old man was rapidly arrested after making what is believed to have been a monkey gesture to Norwich defender Sebastien Bassong after Robert Snodgrass scored his side's fourth goal in the 4-3 win.
The monkey gesture was allegedly made as the on-field celebration was happening and was immediately reported to the referee.
Police arrested the 23-year-old man after he was apparently identified in the crowd from CCTV footage scrutinised by stewards.
"There was an incident after Norwich's fourth goal. Sebastien Bassong made the referee aware there was a racist gesture towards him from a Swansea City fan," a Swansea city spokesman said on Saturday.
"Within 10 minutes of the report the stewards had got hold of the TV footage, replayed it, identified the alleged person in question and within that period he was arrested for a racially aggravated public order offence.
"The matter is with the police, but from the club's point of view we abhor racism and we have worked hard over the years to make this a family club."
A South Wales Police spokesman said: "A 23-year-old man arrested for a racially aggravated public order offence at the Liberty Stadium has been released on conditional bail pending further enquiries.
"Officers are continuing to investigate the incident which took place during yesterday's game between Swansea City and Norwich."