The Cameroon centre-back reported the incident, which occurred after Norwich's fourth goal in a 4-3 victory, to match referee Howard Webb in Saturday's dramatic game at the Liberty Stadium.
Norwich boss Chris Hughton confirmed after the final whistle an investigation was taking place, and the accused person has since been arrested.
"I can only tell you what I have been made aware of, which is that there was a gesture made to Sebastien Bassong," Hughton told Sky Sports in his post-match interview.
"Credit to Swansea City football club, I think they have identified the individual and that is now in the hands of the right authorities."
Bassong scored his third goal in four games to help Norwich to their victory but the win was tainted by the allegations of racism.
And Swansea have condemned the actions of the man who was swiftly arrested after being identified through television footage.
A Swansea spokesman said: "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.
"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. We will look into it and a further statement will follow in due course."
South Wales Police later confirmed the arrest of the 23-year-old in relation to the alleged gesture towards Bassong.
A spokesperson for South Wales Police said: "We can confirm that a 23-year-old Swansea man was arrested during the Swansea v Norwich game at the Liberty Stadium for a racially aggravated public order offence.
"He remains in police custody."