The injury was reported on Wednesday and Tottenham confirmed the news in an official statement on Thursday, adding that the forward will be "monitored by our medical staff ahead of a return to action next season."
A statement read: "The South Korea international sustained the injury after landing on his arm during his national team's World Cup qualifying match against Qatar in Doha on Tuesday, with further assessment and scans confirming that he has sustained a fracture."
Son, who scored 21 goals in all competitions last season, suffered the injury during the 3-2 World Cup qualification defeat to Qatar.
The 24-year-old is now unlikely to be involved when the Spurs squad join up for their 10-day tour of the United States at the end of next month.
Meanwhile, manager Mauricio Pochettino cannot wait for the new campaign to kick off as Tottenham plan for their start to life at Wembley.
Pochettino sees no reason why Tottenham should not expect to hit the ground running and start just as well as they finished the previous campaign.
"We are starting to prepare the season and we cannot wait to start again,'' he said. "This is a moment for our players to enjoy their holidays and try to recharge the batteries, but for us, we are thinking about starting the season in the best condition.
"I am always positive about the fixtures. It is true, the Premier League is tough and we start in Newcastle, and then our first game at Wembley is against Chelsea. I am sure the fans will be excited for that as well."
Information from the Press Association was used in this report.