Etienne Besabesa Mivumbi was arrested on Monday carrying his voice recorder and camera in the northeastern Giteranyi district, local prosecutor Ernest Nduwimana told AFP.
"We charged him with spying because he was a journalist who sought information without accreditation," Nduwimana said, adding Mivumba was being held in custody.
After visiting him in prison Adam Ruhamiriza, of Burundi's Association for the Protection of Human Rights and Detained Persons (APRODH), said Mivumbi insisted he was reporting on agriculture and trade in the Rwanda-Burundi border region.
Burundi has been in crisis since late April over President Pierre Nkurunziza's controversial bid to stand for a third consecutive five-year term, a move branded by opponents as unconstitutional and a violation of a 2006 peace deal that ended 13 years of civil war.
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The government yesterday said protests had ended, and that the remaining demonstrators were only being organised by journalists. Opposition leaders have dismissed the claim.
Several journalists who have been covering Burundi's crisis, which has seen weeks of street demonstrations, a violent police crackdown and a failed coup attempt by a section of the army, have complained of being subjected to threats -- including death threats -- by members of the police or other branches of the security forces.
Relations between Rwanda and Burundi have been tense after Rwanda President Paul Kagame urged Nkurunziza to end his bid for a third term.
According to the Rwanda News Agency, Mivumbi was working for the local Izuba radio and Igihe.Com website.