Nizeyimana, a former army captain and senior intelligence officer, had entered Uganda from the Democratic Republic of Congo on October 1 and was detained in Kampala on Monday, the source said.
He had been extradited to Arusha, northern Tanzania, to the International Criminal Tribunal for Rwanda (ICTR), the source said.
A spokesman for the court confirmed the arrest.
Nizeyimana was among the dozen most wanted suspects sought by the UN court over the genocide in which about 800,000 ethnic Tutsis and politically moderate Hutus were killed.
The United States had offered a $5 million (€3m) reward for his capture. He is charged by the ICTR with genocide, complicity in genocide, and direct and public incitement to commit genocide.
The tribunal says Nizeyimana and others prepared lists of Tutsi intellectuals and those in authority before handing the lists to troops and militia who then killed them.
He is also accused of setting up roadblocks where Tutsis were slaughtered, and of providing weapons and transport to militia in the knowledge they were being used for attacks.
Rwanda’s government, which says Nizeyimana was the main organiser of the genocide in the southern province of Butare, says he has spent the 15 years since the slaughter fighting for a Hutu rebel group in the forests of eastern Congo.
“He was an agitator, a handler, the chief killer in Butare,” Karugarama said. “The arrest of this man... is a very big relief to survivors of the genocide,” said Rwandan Justice Minister Tharcisse Karugarama.