The Spurs star sustained a fracture around his left eye during their 2-1 win at Marseille last week when he collided with Chancel Mbemba (28).
The South Korean skipper and talisman had surgery on Friday and is in a race to be fit for the Qatar World Cup, which starts on November 20th.
"I sent him a message yesterday after the surgery and Sonny was really, really disappointed for this situation," Conte told reporters after Son missed Spurs' 2-1 home defeat to Liverpool on Sunday.
"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."
"I am confident, confident that he can come back quickly and play the World Cup for South Korea," the Italian coach said.
Son is critical to South Korea's chances of making it to the knockout stages at the World Cup, having scored 35 goals in 104 internationals.
South Korea begin their campaign in Qatar against Uruguay on November 24th and also face Ghana and Portugal in Group H.
Son shared last season's Premier League golden boot with Liverpool's Mohamed Salah (30).
