It happened during Norwich's 4-3 defeat at the Liberty Stadium.
The incident took place after Robert Snodgrass had scored Norwich's fourth goal from a free-kick in the 77th minute.
It is believed the Swansea supporter allegedly made a monkey gesture towards Bassong as the Cameroon international went to join his team-mates' celebrations.
A Swansea spokesman: "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 boss Chris Hughton: "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.
"But it should not take away from the fact there were two good teams and two good supports out there today.
"Our support were brilliant in getting behind us and the Swansea supporters were brilliant in getting behind their team, especially in the second half when they thought they could get back in the game."