The arrest warrant was issued by a French judge in 2006 for nine associates of Paul Kagame, the Rwandan president, including Kabuye, over the 1994 plane crash that killed Juvenal Habyarimana, the former president.
"We immediately sent a protest note [to the German embassy in Kigali] ... we emphasised that Rose Kabuye holds a diplomatic passport ... therefore the German government shouldn't have arrested her," Rosemary Museminali, the Rwandan foreign minister, told reporters late on Sunday.
The German ambassador was also summoned.
In a statement, Rwanda's information ministry said the arrests were a "political game designed to blur the truth and weaken the government".
Warning
It said Kabuye had been warned against going to Germany due to the arrest warrants, but she had travelled there and other European countries earlier in the year without incident.
"Kabuye is innocent, which is why she undertook the trip despite warnings, and ultimately why she is ready to face trial in France," it said.
In April, Kagame made a four-day state visit to Germany. According to media reports, Kabuye was on that trip but German law prohibits the detention of any members of an official delegation.
Under French law, a warrant cannot be issued for Kagame because a serving head of state has immunity.
Habyarimana's plane was hit by a missile, and his death triggered the killing of about 800,000 Tutsis and moderate Hutus.
Close ties
Kagame was then leader of the Rwandan Patriotic Front (RPF) which defeated the Habyarimana government's Hutu militias to end the genocide.
Though Rwanda was a Belgian colony until independence in 1962, France kept close links with Kigali from 1975 to 1994, giving financial and military support.
Lef Forster, Kabuye's lawyer, said she had agreed to be transferred to France for questioning over her alleged role in the downing of the plane.
Louise Mushikiwabo, Rwanda's information minister, 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."