The South Korea international was targeted by a fan during Sunday's 2-2 draw at Stamford Bridge and images of the incident have circulated on social media.
Son was preparing to take a corner when the supporter made the gesture, mocking his Korean ethnicity.
Chelsea have previously given out lifetime bans to anyone found guilty of racist abuse inside the stadium and they maintain their stance following this latest issue.
A club statement reads: "Chelsea Football Club finds any form of discriminatory behaviour totally abhorrent. It has no place at Chelsea or in any of our communities.
"Chelsea FC has consistently made its zero tolerance position on discriminatory behaviour very clear, yet there are still idiots like this that attach themselves to this club as so-called ‘fans’, which shames Chelsea FC, our coaches, players, staff and our true supporters.
"We are investigating this incident and, if identified, this individual will face the strongest action from the club."
The unsavoury event marred what was a fantastic afternoon of football.
TUCHEL VS CONTE: ROUND TWO!!! 🤬🤬 pic.twitter.com/XhWuOU4fwD— Sky Sports Premier League (@SkySportsPL) August 14, 2022
Kalidou Koulibaly put Chelsea ahead in the first half before Pierre-Emile Hojbjerg equalised for a rejuvenated Spurs in the second.
This saw tempers boil over on the touchline, with Blues manager Thomas Tuchel and Spurs boss Antonio Conte nearly coming to blows.
James put Chelsea ahead with 13 minutes to go, but Harry Kane popped up with a head in the sixth minute of added time to ensure the points were shared.
Moments before the corner, Spurs defender Cristian Romero pulled the hair of Chelsea wing-back Marc Cucurella, which VAR official on the day Mike Dean admits should've been spotted.
Tuchel and Conte came back for round two at the full-time whistle with both men refusing to let go of their handshake.
Referee Anthony Taylor was given no choice but to send both men off after booking them for their previous altercation.
Featured Image Credit: Alamy
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