Son was forced off during the first half of Spurs' 2-1 win over Marseille on Tuesday that secured their place in the last 16 of the UEFA Champions League.
"We can confirm that Heung-Min Son will undergo surgery to stabilise a fracture around his left eye," Tottenham said in a statement.
"Following surgery, Son will commence rehabilitation with our medical staff and we shall update supporters further in due course."
The Premier League club gave no date for his return, but he faces a race against time to be fit for Korea Republic's opening match of the World Cup against Uruguay on November 24.
We can confirm that Heung-Min Son will undergo surgery to stabilise a fracture around his left eye.— Tottenham Hotspur (@SpursOfficial) November 2, 2022