The Spurs attacker sustained a fracture around his left eye on Tuesday during their 2-1 win at Marseille following a collision with Chancel Mbemba.
It has left Son in a race against time to be available for the tournament in Qatar, which gets under way on November 20.
The 30-year-old had surgery on Friday and therefore missed Tottenham’s 2-1 defeat to Liverpool.
He is also expected to sit out next week’s matches against Nottingham Forest and Leeds but his club manager provided a positive update with South Korea set to begin their World Cup with a Group H fixture with Uruguay on November 24.
“Now, he is at home,” Conte said of Son.
“I sent him a message yesterday after the surgery and Sonny was really, really disappointed for this situation but I hope for him he will recover very well and play in the World Cup.
“I was a player and I know the importance of playing in the World Cup.
“Tonight he was the first person to play this game, for sure he missed us. I am confident, confident that he can come back quickly and play the World Cup for South Korea.”
Son jointly won the Premier League golden boot last season but has struggled for form this campaign and scored only five goals in 19 games in all competitions for Tottenham.