The 24-year-old left the field in obvious pain in the 33rd minute of Tuesday's match in Doha, clutching his right forearm after an aerial challenge.
"He had his right forearm fractured and will undergo surgery by the end of the week," Lee Jae-Chul, spokesman for Korea Football Association told AFP, adding they expect it will take about four weeks for him to recover.
Son has been in sparkling form recently, winning the Premier League Player of the Month for April and becoming the only player to win the award twice last season.
Son ended the campaign with a total of 21 goals in all competitions for Spurs, including 14 in the Premier League, eclipsing the previous single-season scoring record by an Asian player previously held by compatriot Ki Sung-Yeung, who scored eight for Swansea in 2014-15.
Son will return to Tottenham after recovering, Lee said, adding it was unclear whether Son would be fit enough to return to Korea for the crucial final two World Cup qualifiers against group winners Iran on August 31 and five days later against third-placed Uzbekistan.
