All South Korean men are expected to take part in military service before the age of 27 and having just turned 26 the forward is running out of time to earn his exemption.
Son is unlikely to feature in South Korea's opening group match against Bahrain on Wednesday but could play against Malaysia on Friday before the final group game with Kyrgyzstan.
The first knockout round will be played over August 23 and 24 with subsequent rounds every few days until the final on September 1.
Son will certainly miss Tottenham's match this weekend with Fulham and should his country reach the final he will also be unavailable for the remaining matches this side of the international break - against Manchester United and Watford.
Should he escape any injuries, the 26-year-old would likely be back in Mauricio Pochettino's squad for the match with Liverpool on September 15, which is set to be Tottenham's first match at their new stadium.