The striker was dismissed at the end of Brazil's defeat by Colombia on Wednesday for his part in a fracas after the final whistle. CONMEBOL said in a statement it had suspended him "as a consequence of his dismissal and incidents after" the match at Santiago's Monumental Stadium.
Chilean referee Enrique Osses said in his report of the match that Neymar had waited for him in the tunnel and insulted him as he headed for the dressing rooms. CONMEBOL, which also fined the player $10,000, said Brazil had the right to appeal.
The South Americans have one remaining group match, against Venezuela on Sunday and could then face three knockout matches if they reach the final. Neymar was central to the fracas at Monumental Stadium two days ago.
After the final whistle he kicked the ball hard at an opponent. Colombia reacted angrily and almost every player on the pitch was involved in pushing and shoving.
Colombia's Carlos Bacca was also shown a red card and had been suspended for two matches, CONMEBOL said.
Neymar's absence will be a huge loss not just for Brazil but for the entire tournament. Along with Argentina's Lionel Messi, he is the biggest name.
He inspired Brazil to victory over Peru in their first Copa game before being frustrated by the Colombians in a tetchy re-run of their World Cup quarter-final last year.
Neymar was taken off the ground on a stretcher with a broken vertebrae after a clumsy challenge by Colombia defender Juan Zuniga and in his absence, Brazil lost their semi-final 7-1 to Germany.

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