The incident occurred after Norwich scored their final goal in the 4-3 win at the Liberty Stadium, a Robert Snodgrass free-kick.
Bassong made a complaint to referee Howard Webb, who in turn told the fourth official and the man was arrested before the game finished.
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."
Norwich manager Chris Hughton added: "I was made aware at the end of the game there was a gesture made towards Sebastien and I have to say credit to a very good football club in Swansea City. They have identified it and the matter is now with the right authorities and they are dealing with it.
"It is disappointing because it was a wonderful football match out there today but Swansea have dealt with it in the correct way."
Bassong found the net in a victory that extended Norwich's unbeaten Premier League run to nine games.