The Tottenham attacker suffered a fracture around his left eye during a 2-1 win away to Marseille in the Champions League last week.
It raised fears in South Korea that their star player could miss the tournament in Qatar and he had to undergo surgery on Friday.
Spurs boss Antonio Conte confirmed on Sunday it had been a success and that he expected the 30-year-old to be fit for the competition.
But Son himself reiterated on Wednesday he will feature in Qatar, with South Korea set to name their squad later in the week.
"I just wanted to take a moment to say thank you all for the messages of support I have received over the last week," the Tottenham forward wrote on Instagram.
"I have read so many of them and truly, truly appreciate you all. In a tough time I received a lot of strength from you!
"Playing for your country at the World Cup is the dream of so many children growing up, just as it was one of mine too. I won't miss this for the world. I can't wait to represent our beautiful country, see you soon."