Rusesabagina, 66, is accused of being the "founder, leader and sponsor of violent, armed, extremist terror outfits," the agency said.
Authorities in Belgium, where Rusesabagina has ties, told CNN he was not arrested in the country.
Belgium was "notified" Monday by Rwandan judiciary authorities of the arrest of Paul Rusesabagina, the spokesperson of the Belgian Federal Prosecutor Office, Eric Van Duyse, told CNN via email.
"To the best of our knowledge, he was not arrested in Belgium nor transferred from our country," Van Duyse added.
His supporters, and Rusesabagina himself, have long maintained that he became a target of Paul Kagame's government after sustained criticism of Kagame's government and the conduct of the Rwandan Patriotic Front in ending the genocide in 1994.
In a phone interview with CNN from the United States, Rusesabagina's son Trésor Rusesabagina said that he is in shock at his father's arrest.
Trésor Rusesabagina said his mother and sister spoke to his father last Thursday by phone while Paul Rusesabagina was traveling in Dubai.
"That is the last time we talked to him, that is the last time we heard from him and ever since that it has just been silence," he said, adding that he did not know why his father was in Dubai.
CNN has reached out to authorities in the United Arab Emirates, but is yet to receive a response as of late Monday.
Trésor Rusesabagina said the accusations against his father are "patently false" and asked US authorities to intervene.
"Having a thought is a crime in some places, being your own man is a crime in some places, my father is guilty of having the guts to speak up. This is political, of course it is. These are the games they play," he said, referring to the Kagame-led government in Rwanda.
It was during the 1994 genocide that Paul Rusesabagina gained prominence. Around 800,000 Tutsis and moderate Hutus were killed in the genocide, which was led by Hutu extremists.
At the time, he was a manager at the Milles Collines hotel in Kigali where he managed to hide, shelter and save hundreds of people in the luxury hotel during the worst of the killing.
He was the real-life inspiration for the 2004 Hollywood film "Hotel Rwanda," starring Don Cheadle and Sophie Okonedo.
Rusesabagina has not lived in Rwanda since 1996 when he survived an assassination attempt.
He is the recipient of several human rights awards for his efforts during the genocide, including the US Presidential Medal of Freedom in 2005.
---CNN's David McKenzie and Brent Swails contributed to this report from Johannesburg