Son, a South Korean international, was taking a corner in front of the Shed End of Stamford Bridge when the incident occurred during the second half of Sunday’s 2-2 draw.
Images making the rounds on social media seem to show a fan gesturing in a racially offensive manner at the Spurs player as he approached the corner flag to take the set-piece.
According to The Athletic, an inquiry is now ongoing.
Following online harassment directed against Son in April 2021, Manchester United suspended three season ticket holders.
Chelsea has previously taken legal action against fans who have racially insulted rival players.
Raheem Sterling, who has subsequently joined the club from Manchester City, was racially abused by a fan in 2019, and the club banned the fan for life.
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Five further fans were briefly barred from Stamford Bridge for a period of one to two years due to abusive language and aggressive behaviour.
The two London rivals faced off in a heated contest on Sunday at Stamford Bridge, with both managers taking part in the action.
New signature On his home debut, Kalidou Kouliably gave Chelsea the lead with an exquisite volley, but Pierre-Emile Hojbjerg tied the score for Spurs midway through the second half.
Reece James scored his team’s second goal shortly after, giving Chelsea the advantage once more. Harry Kane then rose to score a header in injury time to give Spurs a point.
Following James’ goal, Thomas Tuchel and Antonio Conte got into an argument while segregated on the touchline.
At full-time, after a heated handshake, another argument broke out, and both managers were given red cards for their involvement in the brawl.
The FA is currently looking into Tuchel’s post-game remarks regarding referee Anthony Taylor’s performance.