The incident took place after Robert Snodgrass had scored Norwich's fourth goal from a free-kick in the 77th minute.
Bassong, who had scored earlier in the game, went to celebrate with his team-mates but quickly motioned to referee Howard Webb that he believed he had been the victim of a racist gesture.
Webb then reported the incident to the fourth official, and an arrest of a male supporter has been made.
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."
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It is believed the Swansea supporter allegedly made a monkey gesture towards Bassong as the Cameroon international went to join his team-mates' celebrations.
Canaries boss Chris Hughton admitted he was disappointed by the incident, which overshadowed his side's first away win of the season.
He said: "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 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.
"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."
Bassong gave a statement to police in the immediate aftermath of the game.
The arrest will now sadly cast a shadow over a magnificent game of football that saw the fortunes of both sides swing back and forth before Norwich eventually triumphed.
The Canaries had stunned their high-flying hosts with goals from Steven Whittaker, Bassong and Grant Holt giving them a 3-0 half-time lead.
Swansea rallied through strikes from Michu and Jonathan De Guzman, but Snodgrass made sure of the win with his excellent free-kick, before Michu netted again in stoppage time.
And Hughton was delighted with the character his side showed to stave off the Swansea fightback.
He said: "The first half could not have gone better but it was always going to be difficult to sustain that.
"We did ourselves no favours by conceding so early in the second half, which was always going to give them a lift.
"But at 3-2 a lot of people who were not here would have expected it to go to 3-3 and become a Swansea win.
"We had to dig deep and the character we showed at 3-2 with 30 minutes to go was excellent as it was really tough."
Swansea manager Michael Laudrup, meanwhile, was pleased with his side's reaction to a poor first half, but did not feel they deserved to get anything out of the game.
"We did not play well in the first half today. We were 3-0 down and obviously we came out and had a great reaction in the second half. We scored two and it could have been three but we had an equaliser disallowed.
"But overall we did not deserve it today after the first half. I knew there would be reaction one day after all the positive things people have been saying about us.
"I did not know when it would come but it came in the first half today."