Police initially reported that two nuns were stabbed to death yesterday afternoon. The killer then battered one of the two with a rock, before fleeing the convent.
Italian authorities named the first two killed as Olga Raschietti, 83, and Lucia Pulici, 75, both Roman Catholic nuns.
But in the early hours of Monday morning, another nun in the same convent was killed, her body beaten and head hacked off. Colleagues named her as Bernadette Boggia, aged 79.
According to the diocese of Parma in Italy, they were killed during a botched burglary attempt.
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But Burundi's police said the motive of the killing was not clear, pointing out that no money was taken.
Police spokesman Colonel Helmegilde Harimenshi said all three were raped.
Father Mario Pulcini, an Italian Catholic priest working in the same parish, said after the first two nuns were killed, Boggia had called him in the middle of the night reporting she had heard a noise in the convent.
"The perpetrators had abused her, as they had violated the other two sisters earlier."
Burundian Vice-President Prosper Bazombanza said the government was "appalled by such barbarity", and promised police would do all they could to arrest the killers.
"No one can understand how a third sister was killed late at night... Burundi's government promises to shed light on this matter as quickly as possible," he added.
Italian Foreign Minister Federica Mogherini condemned the attacks.
The suspected killer in the first attack was seen fleeing the convent with a knife in his hand, said Damien Baseka, a local government administrator in Bujumbura.
Police sources suggested the third nun was killed by an accomplice who had hidden in the convent.
Police spokesman Colonel Helmegilde Harimenshi said three men were being questioned.