Panorama examined a document which allegedly encourages secrecy in dealing with cases of priests abusing children.
It says this was enforced by Cardinal Joseph Ratzinger before he became Pope.
The Most Reverend Vincent Nichols, Archbishop of Birmingham, said the claim was "entirely misleading" but the BBC said it stood by the programme.
The document called Crimen Sollicitationis was written in 1962 and apparently instructed bishops on how to handle claims of child sex abuse.
Programme makers asked Father Tom Doyle, a former church lawyer who was sacked from the Vatican for criticising its handling of child abuse, to interpret the document.
He said it was an explicit written policy to cover up cases of child abuse, which stressed the Vatican's control and made no mention of the victims.
The Catholic Church said the document was not directly concerned with child sex abuse, but with the misuse of the confessional.
Archbishop Nichols, speaking on behalf of the Catholic bishops of England and Wales, said of the programme: "It is false because it misrepresents two Vatican documents and uses them quite misleadingly in order to connect the horrors of child abuse to the person of the Pope."
He added that the editing, which used old footage and undated interviews, was misleading, and said the BBC should be ashamed of the standard of its journalism.
Of its viewers, he said: "They will know that aspects of the programme amount to a deeply prejudiced attack on a revered world religious leader."
Cardinal Cormac Murphy-O'Connor, head of the Catholic Church in England and Wales, has written to the BBC's director general, Mark Thompson, to complain.
A BBC spokeswoman said the BBC had a well-defined complaints system and would reply to the letter once they received it.
She added: "The protection of children is clearly an issue of the strongest public interest."