Son was involved in an incident which saw an Edinson Cavani goal ruled out in the first half for the visitors, with Scott McTominay adjudged to have fouled Son in the build-up.
The South Korea forward was targeted with racist insults both in replies to a tweet from Spurs' official account and in the comments section on his most recent Instagram post.
"Another matchday and more abhorrent racial abuse suffered by one of our players," a statement from the north London club read.
"This has again been reported to the platforms and we shall now undertake a full review alongside the Premier League to determine the most effective action moving forward.
"We stand with you, Sonny."
Son became the latest victim in a seemingly endless string of online racist abuse, with Raheem Sterling having received hateful messages in the wake of Manchester City's 2-1 loss to Leeds on Saturday.
Son’s team-mate Davinson Sanchez was recently subjected to racist abuse online, with Spurs boss Jose Mourinho suggesting earlier this week that the club would consider a boycott of social media to take a stand against the problem.
A company spokesperson from Facebook, which owns Instagram, said: “The abuse directed towardsSonHeung-min is abhorrent. We do not want it on Instagram and we have removed a number of comments and accounts that broke our rules.
“We share the goal of tackling online abuse and holding people who share it accountable. We do this by taking action on content and accounts that break our rules and cooperating with law enforcement when we receive a valid legal request.
“We recently announced that we’ll take tougher action when we become aware of people breaking our rules in DMs and we have built tools to help protect people, including the ability to never receive a DM from someone you don’t follow. This work is ongoing and we are committed to doing more.”
Additional reporting by PA.