He has also been fined about N18 million (about 50,000 dollars or 41,121 pounds).
He has seven days to appeal the decision.
Argentina were knocked out in the semi-finals by eventual winners, Brazil.
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Neither Messi nor Argentina's football association have made comments about CONMEBOL's decision.
The only saving grace is that Argentina's qualifying campaign for the 2022 World Cup doesn't begin until March of next year, at which point Messi will be free from the sanctioning.
"Corruption and the referees are preventing people from enjoying the football and they're ruining it a bit", Messi said.
"Throughout the tournament they called bulls**t handballs, bulls**t penalties, and bulls**t fouls".
When asked if he feared being suspended for his statements during the tournament, Messi said "the truth needed to be told".
Messi, Argentina's captain, was red carded for only the second time in his career during the Chile match in Sao Paulo following a scuffle with Gary Medel, who was also sent off.
As punishment for his outbursts, Messi is to serve a three-month suspension from Friday's announcement, ruling him out of Argentina matches until November.