The South Korea international started and completed 89 minutes of the Premier League contest at the Tottenham Hotspur Stadium before being replaced by Arnaut Danjuma.
Son trudged past the Crystal Palace end on his way to the dugout, and a video circulating on social media appears to show one supporter making a racist gesture towards the 30-year-old, who did not react.
Tottenham have now released a statement on the matter, affirming that they are aware of the allegation and are working with the Metropolitan Police and Crystal Palace to identify the individual.
Spurs affirmed that the supporter would be punished with the "strongest possible action" if found guilty of racially abusing Son, saying: "We are aware of an allegation of racial abuse towards Heung-Min Son during yesterday's match.
"Discrimination of any kind is abhorrent and has no place in society, our game and at our Club. We are working with Met Police and Crystal Palace to investigate and identify the individual involved.
"We will do everything in our powers to ensure that if found guilty, the individual will receive the strongest possible action - as was the case earlier this season when Son suffered similar racial abuse at Chelsea."
Back in August, the former Bayer Leverkusen man was also the victim of racist abuse during Tottenham's 2-2 draw with Chelsea at Stamford Bridge as he went to take a corner kick.
Chelsea quickly identified the individual and handed him an indefinite ban six days later, and in March, the 30-year-old was given a three-year stadium ban after pleading guilty to a racially aggravated public order offence.
Six months after the incident at Chelsea, Son was also subjected to "utterly reprehensible" online abuse after coming off the bench to score for Spurs in their 2-0 win over London rivals West Ham United in February.
Harry Kane's 209th Premier League goal - which took him above Wayne Rooney into second place in the all-time charts - propelled Spurs to a one-goal win in Saturday's game, as Ryan Mason picked up his first victory from his second spell as interim head coach.
Tottenham sit sixth in the Premier League table thanks to Saturday's success and are next in action away to fellow European chasers Aston Villa on May 13.