Messi was sanctioned for verbally abusing linesman Emerson Carvalho towards the end of Tuesday's 1-0 World Cup qualifying win over Chile.
No comparto sanción contra Argentina. Algo conozco de fútbol, la infracción fue a #Messi. Mi solidaridad con el mejor futbolista del mundo.— Evo Morales Ayma (@evoespueblo) 28 de marzo de 2017
But according to Morales, the punishment is completely unreasonable and victimises the man he calls the "best player in the world".
"I do not agree with the punishment handed out to Argentina," the head of state wrote on his Twitter page.
"I know something about football, Messi was the man fouled. My solidarity with the best footballer in the world."
Morales has cultivated close ties with neighbouring Argentina since becoming the first indigenous head of state in Bolivian history in 2006.
Diego Maradona is a friend of the president, who was also allied to ex-Argentina chiefs Nestor Kirchner and Cristina Fernandez de Kirchner in regional matters.