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. The first leg in Argentina had ended goalless.
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 Albin'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.
Sao Paulo had dominated the first half with Lucas, playing his final match before joining Paris St Germain, at the heart of everything. He scored the opener in the 23rd minute, pouncing on the ball to fire home after Willian Jose's progress towards goal had been blocked.
Lucas turned provider for the second, playing a fine ball for Osvaldo to run through and lift the ball over Damian Albil, but Lucas had also been on the receiving end of several tough challenges, with one elbow to the face drawing blood.
Fighting then erupted as the players left the pitch at half-time.
Tigre also said their bus was pelted with stones and beer cans on the way to the stadium and Gorosito complained about the treatment his team had received
"We trained two hours away from our hotel, and it took us more than an hour to get to the stadium. We were unable to warm up on the pitch," he said.
Referee Osses said: "We did not see anything, but we have heard some things about what happened. We saw there were some injuries to the Tigre players but I don't know what caused them."
CONMEBOL official Romer Osuna said: "The referee abandoned the game because it was not right to play on. This decision is final. It is a shame that a continental final finished in this fashion."
The Copa Sudamericana is the region's equivalent of the Europa League.
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 against brawling players during a Vasco da Gama-Flamengo derby at the Maracana stadium, where one policeman was seen with his arm around a player's neck.
Two years later Botafogo defender Andre Luis was arrested on the field and frog-marched out of the stadium by around 10 riot police after being sent off in a match at Nautico in the North-Easter city of Recife.
His team-mates were squirted with pepper spray.
Coach Abel Braga said at the time: "It's unbelievable that this happens in the Brazilian championship and in a country which in a few years' time is going to host the World Cup."