Son suffered the injury in Tottenham's final Champions League group stage game against Olympique Marseille on Tuesday which ended in a 2-1 win for the English side to top group.
Son clashed with Marseille goalscorer Chancel Mbemba and had to be taken off in the first half.
The 30-year-old is the main man for South Korea ahead of the World Cup which kicks off on November 20, with the Asian side in the same group with Uruguay, Ghana and Portugal.
A statement issued by the club on Wednesday evening read: "We can confirm that Heung-Min Son will undergo surgery to stabilise a fracture around his left eye.
"The South Korea international suffered the injury during the first half of Tuesday's UEFA Champions League victory at Olympique Marseille.
"Following surgery, Son will commence rehabilitation with our medical staff and we shall update supporters further in due course."
While no timeframe has been given for Son's recovery, he is certain to miss this weekend's Premier League encounter against Liverpool.
Son has five goals in 19 appearances for Tottenham this season.
