Boca Juniors defenders Juan Insaurralde and Jonathan Silva came to blows during the Argentina club's training session on Tuesday morning.
The defenders who were playing with the first team at Boca's practice facility in Buenos Aires, had to be separated by teammates after punching each other.
With TV cameras rolling, both players came face to face and started arguing before the fight broke out.
Various teammates intervened, and manager Guillermo Barros Schelotto threw down his notepad in disgust after sending Insaurralde and Silva to the dressing room.
TV images showed Insaurralde with a torn jersey, while Silva left holding his mouth.
After training, both players appeared at a news conference and apologised.
Insaurralde said: "I want to apologize to Jony [Silva], to my teammates, the technical staff, the fans and the club. What I did wasn't right. It was five seconds of anger."
Added Silva: "It was a moment of madness. It can happen to anyone. It's something that's happened, that's it. It's all good in the group. I apologise for everything."
Boca president Daniel Angelici wrote on Twitter that both players would face punishment for the incident.
"What happened between Insaurralde and Silva in training today cannot be accepted," Angelici wrote. "They are not the proper behaviours of a professional Boca player and for that reason they will be sanctioned."
Boca lead Argentina's Primera Division, which has been temporarily suspended because of a TV rights dispute. Matches are tentatively slated to resume on March 3.