The supporter is alleged to have to have made racial gestures at the Cameroonian Norwich defender, who had earlier scored to put his side 3-0 up at the Liberty Stadium
The 23-year-old man was arrested by police at the Liberty Stadium for a public order offence after Bassong reported the alleged incident to referee Howard Webb on the field of play as his side played out a 4-3 victory against their Welsh hosts.
"A 23-year-old man arrested on suspicion of a racially aggravated public order offence at the Liberty Stadium has been released on conditional bail pending further enquiries," said a spokesperson for South Wales Police.
"Officers are continuing to investigate the incident which took place during yesterday's game between Swansea City and Norwich."
Meanwhile, Swansea have insisted they are happy to help help the Police with their enquiries in any way.
"The club will do everything possible to assist the Police with their enquiries which are on-going," read a Swansea City club statement.
"Swansea City Football Club has worked tirelessly over a number of years to make the Liberty Stadium a family-friendly venue for supporters of all ages, gender and race to attend. It treats seriously all breaches of public order, including racism, which it abhors."
Bassong, who scored his third goal in four games as Chris Hughton's men continued their impressive run of form, has previously been the target of racist abuse on his Twitter account in November.