Son, 24, landed awkwardly during a challenge on Tuesday and will undergo surgery on his right forearm on Friday.
Neither the club nor the Korean FA indicated how long Son will be out for.
Spurs play Paris St-Germain in a pre-season friendly on 23 July and open their Premier League campaign at Newcastle on 12 August.
Son scored 21 goals in 47 games for the north London club last season, as they finished runners-up behind Chelsea in the league.
Tottenham forward Son Heung-min could miss the start of the new season after fracturing his arm in South Korea's World Cup qualifier against Qatar.