"[Kabuye] was arrested on her arrival at the Frankfurt airport. Germany was bound to arrest her by a European arrest warrant issued by France," a German foreign ministry spokesman said.
Lef Forster, Kabuye's lawyer, said that she has now agreed to be transferred to France for questioning over her alleged role in the 1994 downing of a plane carrying Juvenal Habyarimana, Rwanda's then president.
In the wake of the killing of Habyarimana, an ethnic Hutu, Hutu extremists slaughtered about 800,000 people, most of them minority Tutsis and moderate Hutus.
Rwandan denial
The French warrants against Kabuye and eight other individuals suspected of involvement in Habyarimana's death were issued in 2006.
All of those sought by France have close ties to Kagame. Rwanda ended formal diplomatic ties with France after the warrants were issued.
Louise Mushikiwabo, Rwanda's information minister, said that Kabuye was not surprised at being arrested on arrival in Frankfurt.
"She received warnings through the Rwanda government that it had received from Germany two days ago, but it was important for Mrs Kabuye to face this warrant and finally show that she is innocent," Mushikiwabo told Al Jazeera.
"President Kagame has always denounced the fallacy of these arrest warrants. These warrants are politically motivated and were put together by testimony of people who have their own agenda against the Rwandan government.
"In fact, some of the people who testified to the judge have since retracted their testimony."
Kabuye's arrest comes seven months after she visited Germany, as part of an official delegation led by Kagame.
During that visit, Berlin said that it was aware of the warrant, but that its laws prevented the detention of representatives of foreign states on official visits.
Kabuye's arrest on Sunday occurred because she "was at the Frankfurt airport on a private basis", a diplomat told AFP news agency.