Both federation president Ramon Jeserun, 71, and his 43-year-old son Ramon Jamil were arrested after an altercation at the stadium shortly after midnight, according to arrest reports by Miami police, which charged both men with battery.
Jeserun and his son were charged after fighting guards in a tunnel. The FCF said they were only trying to get to the awards ceremony after Argentina beat Colombia in Miami but were prevented due to tightened security measures.
"Employees of the private security of the stadium prevented timely and direct access to the field to most members of the Colombian delegation, despite being duly identified with the official badge of the organization," the FCF said in a statement.
The FCF added that tensions ran high when they were not let through. According to police, Jeserun's son grabbed the guard by the neck and pulled him to the ground, where he punched him and kicked him in the head.
"Ramon Jesurun, driven by his paternal instinct... rushed to complain about what happened but ended up overwhelmed by the situation, as he was in the corridor with his wife, sons, daughters and minor grandchildren," the FCF added.
"As the governing body of Colombian football, we regret this event and offer our apologies to the organizers of the tournament, the host country and the people who were affected.
"For his part, president Jesurun deeply regrets these events, which should never have happened and which resulted in a paternal and instinctive move to protect his son and his family."
Earlier, the final started over an hour late after police initiated a lockdown that left hundreds of fans stuck outside Florida's Hard Rock Stadium.
Dozens of fans were arrested and over 50 people were kicked out from the venue after several fans without tickets tried to enter the stadium.
Argentina beat Colombia 1-0 in the match that was delayed due to the chaos.
