South Korea, ranked 23rd in the world, was beaten 2-0 by 87th-ranked Jordan in the semi-finals of the Asian Football Confederation competition in Qatar.
According to a report from British newspaper The Sun, Son dislocated his finger in a "bust-up" that erupted at dinner the night before the game.
The incident reportedly happened after some younger players on the team - including Lee Kang-in of Paris Saint-Germain - rushed through their meal so they could leave early to play table tennis.
This displeased Son, the team's captain, and some of the older players, as meals on the eve of big games are traditionally seen as a time for bonding.
An unnamed source told the newspaper that when Son asked his younger teammates to sit down, "some disrespectful things were said to him".
"Within seconds, the row spilled into the dining area and players were being pulled apart," the source was quoted as saying. "Son badly injured his finger trying to calm everyone down."
South Korea's Yonhap news agency reported that at first, Son tried to talk to the younger players, but the situation turned physical when they refused to listen.
Son got furious and grabbed Lee, who in turn tried to punch him, Yonhap reported, citing sources familiar with the incident.
The two players had to be pulled apart and Son dislocated his finger in the process.
The Korea Football Association (KFA) confirmed Wednesday that the reports were true.
"It happened when some young players went up to play table tennis, and Son Heung-min and other older players took issue with it," an official was quoted as saying by Yonhap.
"The players exchanged a few words and Son hurt his finger in the process," the official added.
The KFA could not be reached by AFP.
Son was seen playing last week's semifinal in Qatar with two of his fingers on his right hand strapped together.
He has continued to wear the wrapping since returning to Tottenham, where he came on at the weekend in the 2-1 win over Brighton.
South Korea, which was seen as one of the favourites to win the Asian Cup, failed to get a single shot on target during the ill-fated match against Jordan.
Korean football fans have been infuriated by the defeat and have called on the team's head coach Jurgen Klinsmann to resign over his lack of leadership.
The KFA is scheduled to convene a meeting on Thursday to discuss Klinsmann's fate.
