Most Rev Francisco de Assis da Silva told Christian Aid the Brazilian senators' decision to impeach Dilma Rousseff would make poverty and corruption in the country even worse than it already is.
Earlier this week senators voted 61-20 to impeach Ms Rousseff over accusations she used public money to hide budget deficits.
Ms Rousseff has always denied the claims and Christian Aid has said no evidence proving she mismanaged taxpayer's money has been produced.
Reports have said inquiries into the budgetary allegations have also regarded Dilma Rousseff's wider record in government, which has seen long-running strikes, allegations of corruption regarding the country's state-owned oil company and claims Brazil was ill-prepared for the 2016 Summer Olympics.
Most Rev da Silva said: "The Senators condemned the President for a crime but didn't forbid her from running for another public position. This just makes clear that what happened was a coup.
"There was no real crime - just a matter of taking her out of power.
"Our partners abroad have to know how deep are the setbacks we face now.
"We can already name three: the slowing of corruption investigations, setbacks to social rights and increasing private control over Brazil's natural resources and public goods."
The Archbishop added what he believed should be the Brazilian response: "To resist, to resist, to resist. This is how we will face this coup and the setbacks."