The incident, in which Tigre said they were attacked by around 20 men, followed a brawl involving players and officials as the teams left the pitch at half-time in the second leg of the final at Sao Paulo's Morumbi stadium.
It was the latest in a series of controversies involving Brazilian police at matches and comes just 18 months before Brazil hosts the 2014 World Cup.
"They pulled two guns on us, the rest of the match is not going to be played," Tigre coach Nestor Gorosito told Fox Sports.
"They ambushed us and one of them pulled out a revolver and put it against [goalkeeper] Damian Albil's chest. Their security and police also hit us, there were around 20 of them."
Argentine media carried photographs of a blood stained dressing room and comments from players saying they were hit with sticks.
As soon as the referee signalled the end of the match, Sao Paulo players hugged each other and began celebrating. They were then handed the trophy by officials from Conmebol, the South American Football Confederation.
Thousands of celebrating fans then filled one of Sao Paulo's main streets, the Avenida Paulista.
"They were going to lose by a big score," Sao Paulo President Juvenal Juvencio told the club's website. "Our biggest victory is the fact that the Argentines ran away."
Sao Paulo goalkeeper Rogerio Ceni accused Tigre's players of spoiling for a fight.
"They came here to fight, not to play," he said. "We are not worried. I don't know what happened inside the dressing room."
Tigre players remained in their dressing-room for three hours after the incident and then went to a police station to make an official complaint.
A small club based just outside Buenos Aires, Tigre were angry before kick-off after officials tried to stop their players warming up on the pitch. The players managed to dodge officials by leaping over advertising hoardings.
Lucas, in his last game before his move to Paris St Germain, and Osvaldo scored in the space of five minutes to put Sao Paulo in control before fighting erupted as the players left the pitch at half-time.
Tigre also said their bus was pelted with stones and beer cans on its way to the stadium.
RACISM ROW
Brazil has a history of police intervention on the field with one of the most notorious incidents also involving an Argentine side at the Morumbi in April 2005.
Quilmes defender Leandro Desabato was arrested on the field for alleged racism during a Libertadores Cup game against Sao Paulo following a first-half incident with opposing forward Grafite.
Desabato was held in custody for 40 hours, at one stage being handcuffed, before being released. The case was later dropped.
In October 2002, Santos defender Preto was knocked unconscious when a policeman hit him on the head with a truncheon as players protested about a refereeing decision in a match in Belem.
In March 2006, riot police used pepper spray
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