The emotional and sombre mass in a large Roman Catholic church in Burundi's capital was attended by as many as three thousand mourners, including the vice-president and top politicians.
Mourners sobbed as Archbishop of Bujumbura Evariste Ngonagoye praised the life of service the three nuns had given in the impoverished nation, and condemned the "inhuman" crimes of the killer.
The three Roman Catholic nuns were named as Olga Raschietti, 83, Lucia Pulici, 75, and Bernadetta Boggian, aged 79.
Photographs of the elderly nuns were placed on top of three white coffins laid alongside each other in front of mourners, with candles burning alongside.
The three will be buried on Thursday in the nearby town of Bukavu, in neighbouring DR Congo, where their order has a church.
"I loved them, everybody loved them very much…they helped the poor, they have been with us during the hard times of the war," said one mourner, who gave her named only as Alice, who had come from DR Congo to accompany the bodies.
Pope Francis on Monday issued his condolences. "The Holy Father begs the Lord to welcome into his kingdom of peace and light these three faithful and devout nuns," he said in a statement.
Burundian Vice-President Prosper Bazombanza has said the government was "appalled by such barbarity".
Police have arrested a man who they said has confessed to the killing of the nuns in twin attacks in their convent.
On Sunday afternoon two nuns were stabbed to death and the killer then battered one with a rock.
Hours later, before dawn on Monday, another nun in the same convent was killed, her body beaten and head hacked off.
Burundi, a small nation in Africa's Great Lakes region, emerged in 2006 from 13 years of brutal civil war and its political climate remains fractious ahead of presidential polls due in June 2015.
In 2011, a Croatian nun and an Italian charity worker were killed in an apparent botched robbery in northern Burundi.