Barcelona forward Messi, 32, was sent off in Argentina's 2-1 third-place play-off win over Chile and later said the "cup was fixed for Brazil".
He has additionally been fined $50,000 (£41,121) by Conmebol, the South American Football Confederation.
Messi has seven days to request Conmebol's choice to suspend him.
The boycott implies Messi will miss Argentina's up and coming friendlies against Chile, Mexico and Germany in September and October.
Argentina's passing effort for the 2022 World Cup starts in March 2020.
Following Argentina's 2-0 semi-last destruction by hosts Brazil, the Argentine Football Association whined about "genuine and gross refereeing mistakes".
Accordingly, Conmebol said allegations scrutinizing the uprightness of the Copa America were "unwarranted" and "speak to an absence of regard".
Messi was demonstrated a red card in the 37th moment against Chile, following a conflict with Gary Medel, who was additionally rejected.
"We don't need to be a piece of this defilement," Messi said. "They have demonstrated to us an absence of regard all through this competition.
"Unfortunately, the debasement, the refs, they don't enable individuals to appreciate football, they destroyed it a bit."