The incident occurred during Tottenham’s 2-0 Premier League victory over West Ham on Sunday, when substitute Son scored the second goal.
Tottenham announced on Twitter that they had reported the abuse directed at Son.
“We stand with Sonny and urge social media companies and authorities to take action,” they said.
“We have been made aware of the utterly reprehensible online racist abuse directed at Heung-Min Son during today’s match, which the club has reported,” Tottenham added.
Kick It Out, an anti-racism organisation, demanded “meaningful reforms” earlier this month after Brentford striker Ivan Toney was subjected to racial abuse on Instagram.
Toney was targeted following his contentious equaliser against Arsenal, which VAR should have ruled out for offside against teammate Christian Norgaard.
After scoring both goals in a 2-0 league win over Brighton in October of last year, the Brentford forward revealed on Instagram that he had been abused.
At the time, Meta, the parent company of Instagram and Facebook, condemned the abuse but stated that it could not take action because the message had not been reported within the app.
Antonio Neill, 24, of Blyth, Northumberland, admitted at Newcastle Magistrates’ Court in January to sending an offensive message to Toney.