It has been revealed the players quarrelled during a team dinner ahead of their 2-0 semi-final defeat by Jordan last week, which extended their 64-year wait for another Asian Cup title.
"It happened when some young players went up to play table tennis, and Son Heung-min and other older players took issue with it," a Korea Football Association (KFA) official told Yonhap News Agency on Wednesday.
"The players exchanged a few words and Son hurt his finger in the process."
The KFA were not immediately available for comment regarding the incident, but midfielder Lee Kang-in apologised on Instagram on Wednesday.
"We have caused great disappointment to the soccer fans who always support our national team. I'm really sorry," Lee said.
"I should have taken the lead and followed my brothers' instructions, but I'm just sorry for showing soccer fans a bad image. I apologise to the many people who were disappointed by me.
"From now on, I will try to help my brothers become better players and people."
After returning from the tournament in Qatar, Son was brought off the bench by coach Ange Postecoglou in Tottenham's Premier League match against Brighton & Hove Albion on Saturday, with his right index and middle finger strapped together.
The 31-year-old then helped Spurs secure a 2-1 victory with a 96th-minute assist for goalscorer Brennan Johnson, with Postecoglou hailing his captain as "world-class".Â
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