- It says Mr Kayishema and others tried to burn the church down with the refugees inside.
- When this failed, they bulldozed it, burying and killing all those hiding there.
One of four remaining fugitives from the 1994 Rwandan genocide has been captured, UN prosecutors say.
Fulgence Kayishema was arrested in Paarl, South Africa, on Wednesday, the UN court which has been trying the genocide suspects announced.
Mr Kayishema was charged in 2001 over an incident during which more than 2,000 Tutsi men, women and children were burned inside a Catholic church.
Some 800,000 Tutsis and moderate Hutus were killed in the genocide.
In a statement, The Hague-based tribunal - known as the International Residual Mechanism for Criminal Tribunals (MICT) - described Fulgence Kayishema as "one of the world's most wanted genocide fugitives".
It said an international operation involving many countries had made it possible to arrest the man, who had used a number of aliases and false documents.
According to the indictment, Fulgence Kayishema directly participated in the planning and execution of a massacre of refugees hiding at the Nyange church in Kivumu, Kibuye prefecture, on 15 April 1994.
It says Mr Kayishema and others tried to burn the church down with the refugees inside. When this failed, they bulldozed it, burying and killing all those hiding there.
Their corpses were then buried in mass graves.
The Tanzania-based ICTR sentenced more than 60 ringleaders of the genocide, including three over the Notre Dame de la Visitation church massacre.
The church's priest, Athanase Seromba, was sentenced to life in prison in 2008.
The ICTR closed down in 2015, with the remaining cases being taken over by the MICT.