Supreme Court Judge Alexandre de Moraes made the announcement Friday green-lighting Bolsonaro's inclusion in the probe into what the PGR said was the "instigation and intellectual authorship" of the rioting.
In a note seen by AFP Friday, Bolsonaro's defense denied any involvement by the ex-president.
Bolsonaro "never had any relationship or participation in these movements," the note said, blaming the violence on "infiltrators."
Bolsonaro had for years sought to cast doubts on the reliability of Brazil's internationally praised election system, and had suggested he would not accept a defeat.
He never publicly acknowledged new President Luiz Inacio Lula da Silva victory, and left for the United States, where he remains, two days before his successor's inauguration.
As they move to identify the masterminds and financiers of the violent uprising that invited many parallels with the 8 January 2021 storming of the US Capitol, Brazilian authorities on Friday also tightened the screws on a former Bolsonaro minister.
Anderson Torres, who was Bolsonaro's last justice minister, is wanted under a Supreme Court warrant for alleged "collusion" with the rioters.
He also stands accused of "omission" in his most recent job as security chief for the capital Brasilia which was the target of the destructive ire of protesters.
He was fired after the violent revolt against leftist Lula.
Like his former boss Bolsonaro, Torres was in the United States when the riots erupted, and is expected back in Brazil any day.
Lula's new justice minister Flavio Dino, who replaced Torres, said Friday the authorities would give Torres until Monday to present himself.
If he fails to show up, "through international mechanisms, we will launch the procedures for extradition next week, since there is an arrest warrant," Dino told reporters in the capital.
'Cause and effect'
The minister also confirmed the discovery at Torres' home of a draft decree proposing emergency steps for the possible "correction" of the October election that Bolsonaro lost to Lula by a razor-thin margin.
The undated and unsigned draft bears Bolsonaro's name at the bottom, but Dino said the authorship was unknown.
Published in the Folha de S. Paulo newspaper late Thursday, the document foresees the creation of an election "regulation commission" to take over the electoral oversight functions of the Superior Electoral Court (TSE).
The aim, it said, would be "the preservation or immediate restoration of transparency and correction of the 2022 presidential electoral process."
It was not clear whether the document was drawn up before or after Bolsonaro's defeat.
Dino said the document connected some of the dots between Lula's 30 October election victory and the 8 January riots.
It was, he added, a "fundamental element for understanding cause and effect," a "missing link between a succession of events, showing that they were not isolated. And yes, that there was... a plan."
Torres said on Twitter the document was "likely" part of a pile of papers at his home that were destined to be destroyed.
He said the contents of the draft had been taken "out of context" to "feed false narratives" against him.
More than 2,000 rioters were detained after the events, for which the full extent of the damage is still being calculated.