Kwon, currently 112th in the world rankings, lost to Thailand's Kasidit Samrej, who is ranked 500 places below him.
The match in Hangzhou, China saw Kwon lose 3-6 in the first set before winning 7-5 in the second. He then lost the match by losing the third set 4-6.
When the match ended, Kwon smashed his racquet to pieces and refused to shake hands with both Samrej and the referee.
A video of the incident garnered over six million views on Chinese social media. Many said the 25-year-old went into a rage because he missed the chance to be exempted from military service.
Any male South Korean athlete that wins an Asian Games gold medal is exempted from military service. Tennis player Chung Hyeon and football star Son Heung-min have both won the privilege in recent years.
Kwon's defeat has been the biggest surprise of Asian Games men's tennis so far. He was seeded fourth among 16 seeds.
Chinese news site Sohu said Kwon’s rage was also provoked by Samrej’s style of play.
The Thai player often tried to buy time during the game.
He asked to use the restroom after the first set and returned after 10 minutes. In the second set, when he was losing, Samrej called for medical attention to reduce Kwon’s momentum. Kwon argued with the referee and Samrej before losing the third set.
The Korea Tennis Association said they acknowledged the incident but there had yet to be any official discussion of punitive measures against Kwon's action.
On social media, South Korean netizens criticized Kwon and said players like him should not compete in tennis.
Kwon will remain in Hangzhou to play in the men's double competition with his compatriot Hong Seong-chan, the tournament's seventh seed who defeated Vietnam's Ly Hoang Nam in the men’s singles.