According to the investigation, the coup plotters also planned to kill Vice President Geraldo Alckmin and Supreme Court Justice Alexandre de Moraes.
Brazilian media said the five arrested included four military and one police officer.
The police said that five arrest warrants have been carried out, as well as three search and seizure warrants along with other measures, including seizing the suspects' passports and preventing them from contacting others.
Judge de Moraes, who authorised the arrests, said a police investigation revealed the coup plot involved military personnel trained in the army's special forces and a retired high-ranking official.
"The objective was to prevent the inauguration of the legitimately elected government and undermine the free exercise of democracy and the authority of Brazil's judiciary," de Moraes said in the order.
"These actions, peaking between November and December 2022, were part of a broader plan to carry out a coup d'état," he added.
The developments on Tuesday followed statements by two top Brazilian military leaders who declared to police earlier this year that former president Jair Bolsonaro presented them a plan for him to remain in power after the 2022 election, which he lost.
However, both refused and warned him they would arrest him if he tried it, according to judicial documents released in March.
The statements by the two add to Bolsonaro's legal woes as prosecutors seek to find links between the conservative populist leader and the January 8, 2023 riots that trashed government buildings in the capital Brasilia one week after Lula's inauguration.
Lula was informed of the warrants early on Tuesday morning, according to media reports in Brazil, but has not yet commented on the police operation.
The Brazilian president is hosting the final day of the G20 summit in Rio de Janeiro and is expected to hold bilateral meetings with US President Joe Biden and other leaders.
