Copa America organisers CONMEBOL have opened a disciplinary investigation into the "acts of violence" at the end of Wednesday's semi-final between Uruguay and Colombia in Charlotte.
Uruguay's Liverpool striker Darwin Nunez was among the players who waded into the stands at the Bank of America Stadium and exchanged punches with fans during what CONMEBOL called "unacceptable" scenes.
Uruguay central defender Jose Maria Gimenez said players had leapt into the melee out of concern for the safety of family members and loved ones watching the game in that section of the ground.
Uruguay are scheduled to face Canada, at the same stadium, in the third place game on Saturday and it remains to be seen if any of their players are suspended for that game.
"In light of the acts of violence that occurred at the end of the match between the national teams of Uruguay and Colombia, the Disciplinary Unit of CONMEBOL has decided to open an investigation to clarify the sequence of events and the responsibilities of those involved," the South American confederation said.
CONMEBOL said they would not accept any repeat of the incidents, which saw fighting between the two sets of supporters, for Sunday's final between Argentina and Colombia at Hard Rock Stadium in Miami.
"On the eve of our Copa America final, we want to reaffirm and warn that no action that tarnishes a global football celebration will be tolerated, involving both the protagonists and the fans present in the stadium for a final viewed by hundreds of millions of spectators worldwide.
"It is unacceptable that an incident like this turns passion into violence. Therefore, no behaviour that violates the spirit of the sport and the world's most beautiful spectacle, which belongs to the whole family, will be tolerated," they added.
Gimenez said that the players had got involved to protect their family members and was critical of the local police in the venue.
"Our family was in danger. We had to go to the stands to take out our loved ones, with tiny newborn babies," the Atletico Madrid player said.
"There was not a single police officer... I hope those who are organising this are a little more careful with the families," he said.
As well as the incidents in the stands, there were also clashes on the field at the final whistle involving players from both teams.
MB