Son, left the field in obvious pain in the 33rd minute of South Korea's 3-2 World Cup qualifying defeat to Qatar.
"The operation was successful," KFA Spokesman Cho Jun-Heon told AFP, adding that Son will stay in South Korea to focus on his recovery.
Son, 24, left the field in obvious pain in the 33rd minute of South Korea's 3-2 World Cup qualifying defeat to Qatar on Tuesday, clutching his right forearm after an aerial challenge.
The operation at a university hospital lasted about an hour, and Son had the broken bones repaired with pins and metal plates to keep them in place, the Sports Chosun daily reported.
While the KFA estimated Son's recuperation would take about a month, Song Jun-Seop, a former national team doctor, gave a longer recovery time of at least 12 weeks, according to the daily.
The new Premier League season kicks off in eight weeks' time, on August 12, and South Korea have crunch World Cup qualifiers on August 31 and September 5.
His absence would be a further blow to South Korea, whose first defeat to Qatar in 32 years put their hopes of automatic qualification for a ninth consecutive World Cup finals in Russia next year on a knife-edge.
The KFA on Thursday fired coach Uli Stielike after the shock defeat which left them clinging to the second automatic qualifying spot in Group A.
Son has been in sparkling form, winning the Premier League player of the month award for April and ending the season with a total of 21 goals in all competitions for Spurs.