Bolsonaro, knows as "The Brazilian Trump", was being carried on the shoulders of a supporter when he was attacked, authorities said.
A leaked extract of the the suspect's interview to Brazilian online media site G1, claims that he was ordered by God to carry out the attack. Other videos show supporters carrying him to a vehicle.
Police spokesman Flavio Santiago told the AP that Bolsonaro's attacker was arrested shortly after the stabbing.
One supporter camped outside Bolsonaro's hospital room, Bruno Engler, 21, who is running for a Minas Gerais state congressional seat on Bolsonaro's Social Liberal Party, said if he could, he would lynch the suspect.
Bispo de Oliveira acted "for religious reasons, for political reasons, and also because of the prejudice Bolsonaro has always shown when he talks about race, religion and even women", said his lawyer, Pedro Augusto Lima Possa.
Flavio Bolsonaro, son Jair Bolsonaro, gestures outside Santa Casa hospital where his father was being treated in the southeastern city of Juiz de Fora on Friday.
Flavio said the puncture had hit parts of his father's liver, lung and intestines and he lost a lot of blood. "He lost a lot of blood, arrived at the hospital. nearly dead". "His condition now seems stabilized". Still, analysts said Thursday's attack may give his candidacy a fresh momentum.
In spite of Mr Bolsonaro's lead, support has plateaued in recent weeks and polls show him losing in a run-off to most rivals. However, despite his seemingly high popularity, Bolsonaro have so far failed to form any alliance with any major political forces in Brazil so far.
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In March, Ms Holmes settled charges with the Securities and Exchange Commission, a top United States financial regulator. Holmes, who did not admit wrongdoing, was fined $500,000 and ordered to relinquish 18.9 million shares in the company.
Brazil's President Michel Temer commented on the attack during an event in the nation's capital, Brasilia, saying "the intolerance that there's been in Brazilian society is unacceptable".
Bolsonaro is second in the polls; in first is former President Luiz Inacio Lula da Silva - who is now in jail on corruption charges and has been banned from the race.
Despite being a congressman since 1991, Bolsonaro is running as an outsider ready to upend the establishment.
While Mr. Bolsonaro has a strong following, he is also a deeply polarising figure. Lula appealed the electoral court decision that denied his candidacy, but on Thursday, Brazil's Supreme Court rejected it, effectively putting an end to the former president's hopes.
But he doubted there would be a big shift his way, especially given that 44 percent of those surveyed in the latest Ibope poll say they would never cast a ballot for Bolsonaro, the stiffest rejection for any candidate. The comment prompted an immediate rebuke from the attorney general, who asked Bolsonaro to explain that comment.
The attack comes at a time of increasingly heated rhetoric, and sometimes violence, related to campaigns and candidates.
Fernando Haddad, who will likely be the leftist Workers Party presidential candidate, said the stabbing was a "shame" and a "horror".