It is an artistic protest at the deepening political crisis in Brazil.
The anonymous artist said he wanted to protect national figures from Brazil's history from seeing the shameful state of the nation.
The artist said the work was not connected to protest marches against President Dilma Rousseff planned for Sunday.
The statues, which are scattered across the city,  include one of Brazil's ex-President Getulio Vargas, the country's first dictator who ruled the country from 1930 to 1945 and sought to transform Brazil from a plantation-based economy into an industrial powerhouse.
Also blindfolded was a statue of Alberto Santos Dumond, the father of  Brazilian aviation and Isabel, Princess Imperial of Brazil who as regent actively promoted and ultimately signed the  "Lei Aurea" or Golden Law, emancipating all slaves in Brazil on 13 May 1888.
The artist who works under an art scheme called "Project Oraculo" said that he wanted to transmit that "protest is not just about street demonstrations".
On Sunday huge protests are planned by opponents to President Dilma Rousseff to demand her impeachment on charges of having mishandled the budget and the economy.
Brazil is suffering its worse economic recession in decades.
The artist said:  "The idea is to blindfold the eyes of those who can no longer do anything for the country and to avoid them helplessly witnessing the economic and political crisis in the country, unable to do anything."
A hundred statues on the streets of Rio de Janeiro have had their eyes covered in red blindfolds.