The 22-year-old midfielder was among a group of younger members of the South Korea squad that left dinner early to play table tennis on the eve of their Asian Cup semi-final clash with Jordan.
South Korea captain Son was incensed by the premature exit and confronted Lee before a brawl broke out.
Dispatch reported that Son grabbed Lee by the collar before the PSG man responded by punching the 31-year-old in the face.
The resulting melee saw Son sustain a nasty injury after getting his finger caught in another person's clothing.
Lee took to Instagram to apologise for his part in the scuffle but just as the incident appeared to cool, a spokesperson for a law firm representing Lee, issued an official statement to the press refuting the allegations against him.
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The statement read: "Lee Kang-in is deeply regretting and reflecting on his mistakes. Once again, he apologises for causing discomfort and concern to many soccer fans.
"Considering that he was at the centre of the dispute, Lee Kang-in believed that an apology, rather than providing specific details of the incident, was the most appropriate course of action.
"However, recent articles, including those from Dispatch, contained inaccurate information which is being exaggerated and reproduced as if it were true.
"Therefore, it is necessary to correct any misinformation.
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"1) The articles stating that Lee Kang In threw his fist in Son Heung Min's face when Son Heung Min grabbed his collar are different from the truth.
"2) During the table tennis incident, there were also senior players present, and table tennis had been a common activity prior to that day.
"We will clarify and address the remaining issues at a later time.
Once again, sincere apologies to everyone who has been disappointed by Lee Kang In."
On the pitch, South Korea were subsequently beaten 2-0 as Jordan sprung a major semi-final upset.
Jurgen Klinsmann's side failed to register any shots on target against the side ranked 64 places below them.
South Korea had been one of the favourites to lift the trophy but a poor semi-final display saw them crash out pf the tournament with host nation Qatar going on to beat Jordan in the final.