The manifesto, signed by some 3000 leading Brazilian figures, did not mention Bolsonaro by name, but clearly addressed the situation he has caused by questioning the voting system ahead of the October 2 election and attacking Supreme Court justices who oversee the elections in Brazil.
Their letter referred to "unfounded attacks" on the voting system, which Bolsonaro claims is vulnerable to fraud, and "insinuations" the election results will not be respected.
Among those to sign the manifesto were former central bank president Arminio Fraga, former finance minister Pedro Malan and six former justices of Brazil's Supreme Court.
Bolsonaro, who is trailing leftist former president Luiz Inacio Lula da Silva in the polls, has frequently criticised the voting system and proposed the armed forces be involved in counting the votes.
He has called for protests on September 7 to back his allegations, less than a month before election day, raising fears he will refuse to accept defeat and could try to trigger a coup or encourage a mob of supporters to take to the streets.
"We should now be at the height of democracy, with different political projects vying to convince voters which is the best direction for the country to take in the next few years," the manifesto said.
"Instead, we are facing a moment of immense danger for our democratic institutions and insinuations of contempt for the result of the elections," the letter said.
The signatories said Brazil's electronic voting system has been an example for the world, ensuring the election of alternating parties in power in a safe and reliable way.
"In today's Brazil, there is no more room for authoritarian setbacks," the letter said, recalling dictatorship and torture Brazil has suffered in the past under military rule.
Bolsonaro's chief of staff, Ciro Nogueira, responding to the proclamation, said on Twitter bankers were upset with the president because he had established the independence of the central bank.Â
Financial insitutions had lost more than 30 billion reais ($A8.1 billion) in transaction fees due to a new system for electronic payments, he said.