Son (centre) was alleged to have been abused as he took a corner at the Shed End of Stamford Bridge
The incident is alleged to have happened when Son went to take a corner in the second half during Sunday's 2-2 draw in the Premier League.
The club have previously banned fans for life following racist incidents.
In a statement, Chelsea said discriminatory behaviour was "totally abhorrent".
It added: "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.
"It has no place at Chelsea or in any of our communities."
Chelsea's long-running 'No To Hate' campaign launched its latest initiative on Sunday, which gives instructions on the back of every seat on how supporters can report alleged abuses by either by text or by barcode on a smartphone.
They believe that identifying a specific seat from which incidents either happen or are reported will help increase the chances of individuals being caught.
-- Courtesy of BBC Sport