Bunyoni was prime minister from mid-2020 to September 2022 but was fired in a high-level political purge after President Evariste Ndayishimiye took office.
A former police chief and minister of internal security, he was replaced by then interior minister Gervais Ndirakobuca, days after Ndayishimiye had warned of a "coup" plot against him.
He was arrested last month in the city of Bujumbura on the eve of his 51st birthday.
"Everyone was surprised to see him arrive handcuffed," a witness told AFP on condition of anonymity, adding that he was clad in the green uniforms worn by Burundian prisoners.
Monday's session held before a council chamber extended his pre-trial detention at Ngozi Prison in the north of the country, a judicial source who asked for anonymity to discuss the case told AFP.
The former premier was charged on Friday before a three-judge high court in a closed session, the source added.
Bunyoni is accused of "undermining the internal security of the state, undermining the proper functioning of the national economy and illegal enrichment", according to court documents seen by AFP.
He is also facing charges of illegal possession of weapons and insulting the president.
He was seen as the head of a cabal of military leaders known as "the generals" who wielded the true political power in Burundi and the president himself had alluded to his isolation in a 2021 speech.
Ndayishimiye took power in June 2020 after Nkurunziza died of what the Burundian authorities said was heart failure amid widespread speculation he succumbed to Covid-19.
He has been hailed by the international community for slowly ending years of Burundi's isolation.
But he has failed to improve a wretched record on human rights and the country of 12 million people remains one of the poorest on the planet.
Burundi had been under US and EU sanctions over a bloody crisis that erupted in 2015 when Nkurunziza made a bid for a third term in office.
The turmoil claimed the lives of 1,200 Burundians and saw 400,000 flee the country.