“He was on a spying mission and it was the third such mission he carried out in Burundi,” said Nkurikiye, who added that the missions were intended to “destabilise” the country.
Relations between Burundi and Rwanda are at a low ebb, with Bujumbura and the United Nations accusing Kigali of supporting Burundian rebels.
Burundi was plunged into crisis following President Pierre Nkurunziza’s bid for a third term which he went on to win in a July 2015 election.
The man, in his thirties, wore a red tracksuit and had no visible signs of abuse, according to an AFP photographer.
He “confessed” to journalists in kinyarwanda, an official language in neighbouring Rwanda, accepting that he had entered the country for the purposes of espionage.
The man previously entered Burundi in May 2015 to help extract the plotters of a failed coup, and once again in November 2015 to gather information for attacks against VIPs in the country, according to Nkurikiye.
He was presented to the media at the offices of the National Intelligence Service (SNR), an agency regularly accused of human rights abuses, torture and extra-judicial killings.
Officials alleged that his latest mission in Burundi was to negotiate with an order of nuns to determine if they would be willing to hide 200 fighters involved in attacks in the country.
More than 400 people have been killed since the violence erupted in April and more than 240,000 have fled.
Thousands of Rwandans who lived in Burundi have fled the country since the start of the crisis after several arrests within their community.