Victims' rights groups and others said the comments made by Napier, the Catholic Archbishop of Durban, were insensitive, especially given perceptions the Catholic Church has not done enough to root out abuse.
"I apologise sincerely and unreservedly to all who were offended by the botched interview, and especially to those who have been abused and need every help and support that the church can give," Napier said in a statement on Monday.
Napier, one of the 115 cardinals who took part in the Vatican conclave that elected Pope Francis, told BBC Radio 5 that paedophilia was a "disorder" that needed to be treated.
"From my experience, paedophilia is actually an illness. It's not a criminal condition, it's an illness," he said.
He also said he knew of at least two priests who became paedophiles after they were abused as children and therefore required treatment, not punishment. "That's when the wheels came off. I now stand accused of saying that paedophilia is a mental condition or disorder and not a crime," Napier said in his statement.
"Child sexual abuse is a heinous crime among other things because of the damage it does to the child. In that concern I include the abused who has become an abuser."
One prominent South African presenter, Justice Malala, named Napier "loser of the week" on his television show and said the cardinal's remarks were an embarrassment to Catholics.
Francis, the first non-European pope in nearly 1 300 years, has signalled a sharp change of style from his predecessor, Benedict, for the 1.2-billion-member church, which is beset by scandals, intrigue and strife.
He said on Saturday the church should be poor and remember that its mission is to serve the poor. – Reuters