Bishop of Norwich, Rt Rev Graham James, who comments on media issues for the Church of England, was quoted by the Sunday Times as saying: "It is a failure of the BBC as a public service broadcaster."
He spoke after director of factual at BBC Studios, Lisa Opie, warned staff in a leaked email the recent loss of the contract to produce Songs of Praise "means we will no longer have a permanent religion and ethics department in Salford."
Bishop Graham said it was a "strange" decision, given the BBC's pledge to the watchdog Ofcom - which begins regulating the corporation on Monday - that it would boost religious programming.
The BBC refused to say how many staff it now has in religion and ethics or how many might be lost following the changes; however, it did confirm an undisclosed number would remain.
Religion is only the latest area to experience cuts under a requirement the BBC puts programmes out to tender.
A BBC spokesman told Premier: "BBC Studios will continue to have a religion and ethics team, as part of its Pacific Quay Productions unit, making and producing top quality religious and ethics programming and we also have a wealth of religious broadcasting expertise within news, radio and the World Service.
"It is a requirement of the new Charter that we commercially contest long running programmes. It's not something we can simply decide not to do.
"However, Songs of Praise remains firmly at the heart of our schedule, and in the coming days we'll announce exciting new commissions for Easter.
"While we already do more than any other broadcaster, we've been clear that we want to do even more for all faiths, including Christianity. hat's why we have already announced a review some months back into how we can deliver even more.
"Ofcom's draft operating licence, which we welcomed, is consulting on more hours of religious programming and has nothing to do with who makes the programmes."