Messi, 32, accused CONMEBOL of corruption after he was sent off against Chile in the third-place playoff match during the tournament in Brazil, which ended last month.
Messi was angered by two incidents during the Copa.
Argentina was denied two penalty claims in its 2-0 semifinal loss to the hosts, after which Messi claimed Brazil was “managing a lot in CONMEBOL these days.” And when he was harshly dismissed in the next game, which Argentina won, 2-1, he could not contain his anger.
“Corruption and the referees are preventing people from enjoying the football, and they’re ruining it a bit,” Messi said.
He was given his marching orders after a first-half scuffle with Chile’s captain, Gary Medel, although television images suggested he had done little wrong.
In a statement on its website, CONMEBOL did not specify why Messi was being punished but said the punishment was related to articles 7.1 and 7.2 of the organization’s disciplinary regulations.
One clause refers to “offensive, insulting behavior or making defamatory protests of any kind.”
Another clause mentions “breaching the decisions, directives or orders of the judicial bodies.”
The ban means that Messi will miss only a handful of friendly matches. Argentina’s next competitive match is not until the South American qualifiers for the 2022 World Cup in Qatar begin in March.
However, he will miss the first of those because he received a one-game ban from CONMEBOL for his red card against Chile.