Bob Rugurika, director of the popular independent African Public Radio (RPA), was arrested in mid-January after broadcasting the purported confession of a man claiming he was one of the killers.
The three Roman Catholic nuns, Lucia Pulici, 75, Bernadetta Boggian, 79 and Olga Raschietti, 83, were murdered at a convent in Kamenge, north of the capital Bujumbura in September last year. The purported confession contradicted a police account of the crime and implicated a top official.
Speaking on Catholic station Radio Maria, prominent cleric Pierre Antoine Madaraga said he was "hurt" by the arrest and said the report by RPA - which is close to the opposition and known for its crime reporting - should be followed up.
Police arrested a suspect two days after the crime and said he had owned up to the murders. They also presented the suspect as being mentally unstable.
"When RPA started to give us other information, we thought that finally there is another lead to follow," Madaraga said. "So putting RPA's director in prison is like wanting to silence the truth."
"I'm asking seriously that we free him so the truth can be told about the murder of the three sisters," he added.
For broadcasting the counter-confession and refusing to give up the self-proclaimed killer, Rugurika was charged with complicity in the murders, "breach of public solidarity" and disclosing confidential information regarding a case.
He faces up to 20 years in prison if convicted.
The man who made the radio claim said he was ordered to carry out the hits by three men he met in a bar belonging to former spy boss, Adolphe Nshimirimana.
Nshimirimana, who now works in the presidency, is one of President Pierre Nkurunziza's top lieutenants.
The killing of the nuns caused shock in Burundi and Italy. Two were stabbed to death and the third decapitated.
Burundi, a small nation in Africa's Great Lakes region, emerged from 13 years of brutal civil war in 2006, but the political climate remains fractious ahead of presidential polls due in June.