A Miami-Dade County police file indicated Jesurun had been arrested on charges of "assault on officer/employee" on Sunday night at Hard Rock Stadium.
Security guards refused Jesurun access to the field, with his son and other family members, for the awards ceremony after Argentina defeated Colombia 1-0, a scuffle broke out and Jesurun and his son were arrested, Colombian newspaper El Tiempo reported.
"This badge says 'full access' and a security guard ... disregarded it," Jesurun said, pointing to his official credentials after he was released having reportedly posted $2,000 bail.
"I insisted (to the security guard) that I should enter and he pushed me and a ridiculous, unnecessary melee broke out," the 71-year-old Jesurun told the El Heraldo newspaper.
There was chaos at the match, which was delayed by 82 minutes, as spectators stormed the gates at the home of the NFL Miami Dolphins, with people pushed to the ground and others trying to sneak into the stadium through air-conditioning ducts.
Argentina won the match with a goal in extra time by Lautaro Martinez.
Police said there were 27 arrests and 55 ejections from the stadium.
"I'm very proud of our officers' response to a volatile situation and for their hard work in keeping our community safe as well as our law enforcement partners who provided key support," said Miami-Dade police director Stephanie Daniels.
South American football governing body CONMEBOL suggested security procedures, such as setting up an outer perimeter to screen ticketless fans, had not been followed by organisers.
"Fans without tickets went to the vicinity of the stadium, which delayed the normal access of the people who did have them, which slowed down the entry and determined the closing of doors," CONMEBOL said in a statement.
"We regret that the acts of violence produced by malicious people have tarnished a final that was ready to be a great celebration of sport."
The Copa America had been marred by earlier incidents off the pitch.
On Wednesday, Uruguay players were involved in a brawl with Colombian fans in the stands after their 1-0 semi-final defeat.
