The complaint was met with skepticism by election authorities and other political figures who have recognized Lula's victory.
The head of Brazil's Senate, Rodrigo Pacheco, said the election result was "unquestionable," while the center-right Brazilian Social Democratic Party (PSDB) called Bolsonaro's challenge "senseless."
When the PSDB challenged the result of the 2014 presidential election, the investigation took one year and no irregularities were found.
Vice President Hamilton Mourao, on a trip to Portugal, acknowledged on Wednesday that Bolsonaro's challenge was unlikely to succeed but said Brazil's electoral process needed more "transparency."
Analyst Andre Cesar at Hold Legislativa consultancy said, however, that the challenge would provide ammunition for an ongoing protest movement of Bolsonaro's hardcore supporters.