Mr Bolsonaro’s supporters trashed Brazil’s highest seats of power, breaking windows, toppling furniture, and smashing computers and printers during a wave of unrest last Sunday.
The rioters, decked out in Brazil’s iconic yellow-and-green national football shirt, which they have adopted as their unofficial uniform, overwhelmed the capital Brasilia, where they stormed the congress building, the supreme court and the presidential palace.
Their aim was to depose the recently inaugurated president, Luiz Inácio Lula da Silva, and reinstate Mr Bolsonaro who had lost a close and bitterly divisive election last October. A vote which his backers, again echoing Donald Trump, claimed was stolen by fraudsters.
"Public figures who continue to cowardly conspire against democracy trying to establish a state of exception will be held accountable," said Justice Alexandre de Moraes, who agreed to the request by federal prosecutors to launch a probe into the incident.
Mr Bolsonaro, who is currently in the United States, will be investigated by prosecutors for possible "instigation and intellectual authorship of the anti-democratic acts that resulted in vandalism and violence in Brasilia last Sunday," the top public prosecutor’s office said in a statement.
The Supreme Court had already ordered the arrest of Bolsonaro’s former justice minister, Anderson Torres, for allowing the protests to take place in the Brazilian capital after he assumed responsibility for Brasilia’s public security.
Torres, who like Bolsonaro is in Florida, has said he plans to return to Brazil to turn himself in. Bolsonaro said on social media he will move forward his return to Brazil.
Justice Minister Flavio Dino told a news conference he would wait until next week to re-evaluate Torres’ case, indicating that an effort to request his extradition could happen if the former minister does not turn himself in.
The arrest warrant against Torres was issued by de Moraes, who removed Brasilia’s security chief from his post just hours after the rampage.
On Thursday, police found a draft decree in Torres’ house that appeared to be a proposal to interfere in the result of the election. Torres claimed the document was among others in a stack that was being thrown out. He said they were "leaked" to Folha de S.Paulo newspaper in his absence to create a "false narrative."
Dino said he has made no requests to the United States regarding Bolsonaro.
The political party to which Bolsonaro belongs, the right-wing Liberal Party (PL), decided to beef up its team of lawyers in preparation for the defence of the former president, a party official told Reuters.
Mr Bolsonaro faces several investigations for anti-democratic statements he made as president, including repeated claims that the election system was open to fraud.
PL party leaders now fear he will be held responsible for Sunday’s storming of government buildings. While they do not think he will face arrest, they fear he could be declared ineligible to run in the 2026 election, the official said.