South Korea international Son was allegedly targeted during the Premier League game against Manchester United at Wembley.
A Spurs season-ticket holder who was at the game made the allegation via social media.
The fan said a derogatory term was used towards Son and came from a supporter in the Tottenham section of the Wembley crowd.
Tottenham confirmed the club is investigating the alleged offence.
United won the game 1-0 thanks to a goal late in the first half scored by Marcus Rashford.
Son has been a key player for Spurs this season, scoring eight Premier League goals in 17 appearances.
The 26 year-old forward travelled to the United Arab Emirates after the United loss to join his South Korea team-mates for the Asian Cup.