The violence happened in the west-central state of Mato Grosso after tempers frayed during an argument over support for the two candidates.
Bolsonaro trails Lula in the polls in an election riven by intense polarization.
According to the police report of the incident, Rafael Silva de Oliveira, 24, killed Benedito Cardoso dos Santos, 42, by stabbing him with a knife.
The suspect was taken to the police station, where he confessed and was charged.
Speaking with reporters in Rio de Janeiro on Friday, Lula commented on the stabbing, saying there was a "climate of hatred in the electoral process which is completely abnormal".
Lula also suggested law enforcement should investigate whether such incidents "had been ordered, or guided, or if it is a political strategy".
He did not provide any evidence to back up the suggestion of orchestrated attacks.
In a statement, Juanita Goebertus Estrada, the director of the Americas for Human Rights Watch, said "all candidates should energetically condemn" the killing of Cardoso dos Santos, adding that "Brazilians deserve peaceful elections and should be able to engage in political discussions without fear of violence or retaliation for their views".
The president's office did not immediately respond to a request for comment.
In July, a similar incident occurred when a local official from Lula's opposition Workers' Party was shot dead by a federal prison guard shouting support for Bolsonaro.
On Friday morning, a Bolsonaro supporter was left with a head wound and said he had been assaulted by supporters of the Workers Party who were waiting for Lula to arrive at an event with evangelicals in the city of Sao Goncalo, in Rio de Janeiro state.
Bolsonaro, who has long railed against Lula and his leftist allies, has floated the idea of not accepting any election loss, citing unfounded claims of election fraud and problems with Brazil's widely respected electronic voting system.
Lula on Friday described him as a "ruder, less civilised and a bad copy", of former US president Donald Trump, who has refused to accept the results of the 2020 election.
