The decisive leg had been set to be played on Saturday but was suspended until Sunday after Boca players were injured when their bus was attacked by River fans outside their Monumental stadium in Buenos Aires.
"We don't want there to be any excuses that conditions were not equal for both teams," Alejandro Dominguez, the president of the South American football confederation CONMEBOL, said on TV. "We want both teams to have time to recover."
"A sad day for South American football," he later tweeted.
CONMEBOL said officials would meet with the heads of both clubs on Tuesday to discuss a date for rescheduling.
Saturday's mayhem and questionable management of the stadium caused a national outcry. "Embarrassing" rang out top headline of the news site of local paper Clarin. The front page of a Peruvian sports tabloid called El Bocon went with a blunt one-word headline: "IDIOTS".
The stadium was shut for several hours late on Saturday when city authorities said it apparently violated safety rules by allowing too many fans to enter, and by locking emergency exits.
Early on Sunday the Boca Juniors club requested the second leg of the Copa Libertadores final be suspended, saying the game could not take place unless conditions were equal for both teams.
It was the first time Argentina's two biggest clubs had met for the title. The crosstown showdown had been billed as the greatest final in the competition's 58-year history.
But Saturday's scheduled final will instead be remembered for the violence that left players bleeding and almost all the windows on one side of the Boca bus shattered.
The incident was a black eye for some of the Argentine security forces who will be responsible for keeping the city calm during a meeting of the leaders of the G20 bloc of industrialised nations on Friday.
"We are prepared for the G20. We have faith," Jorge Faurie, Argentina's foreign minister, said on television.
Faith in CONMEBOL was meanwhile running short among fans.
"We're furious. You waste so much time and money. It takes a while to get here. The police treat you badly. You have to park far away. You don't know if your car is going to get broken into," said Ayrton da Silva, who was at the stadium when the postponement was announced.
"CONMEBOL's organisation?" said his exasperated father Luiz da Silva. "The likelihood of this game being postponed was 85 per cent. How do you take this decision now? It should have been made at 10 o'clock this morning. But well, this is Argentina."
Some fans came from overseas to see the game. City authorities scrambled to explain what had happened.
"There is something that is very difficult to guard against. Human stupidity," Buenos Aires Mayor Horacio Rodriguez Larreta told reporters. He blamed soccer hooligans, known as the "barras bravas" in Argentina for the mess.
"They are the mafia of Argentine soccer," he said.
(Reporting by Andrew Downie; Additional reporting Hugh Bronstein; Editing by Daniel Flynn, Phil Berlowitz and David Gregorio)
