Messi was sent off against in the Copa America third-place playoff and afterwards alleged that the tournament had been fixed in favour of hosts Brazil, who beat Argentina in a controversial semi-final on their way to the title.
The Argentina captain called the South American Football Confederation (CONMEBOL) "corrupt" and did not attend the ceremony to pick up his medal. He was handed a one-match ban and a $1,500 (£1,233) fine for his sending off last month.
CONMEBOL had said that the Barcelona forward's comments were "unacceptable".
"The player is suspended to play official and friendly matches with his national team in that period of time," the organisation said in a statement on Friday.
The ban means Messi will miss Argentina's upcoming friendlies against Chile and Mexico in the United States in September and another against Germany in Dortmund on October 9.
He can appeal against the latest sanctions within seven days.