President Lula has said he suspects members of the armed forces colluded with protesters.
He has dismissed dozens of military officers in recent days.
Thousands of supporters of Mr Bolsonaro stormed government buildings in BrasÃlia on 8 January after managing to march, largely unchallenged, through the city.
Brazil's president, Luiz Inácio Lula da Silva, has sacked the country's army chief, two weeks after rioting in the capital. General Julio Cesar de Arruda had only been in the role since 30 December - just before former president Jair Bolsonaro's mandate ended.