Archbishop Philip Wilson is the most senior Catholic clergyman in the world to face such a charge.
But some Catholics are defending his reaction to the charge.
Archbishop Philip Wilson has been charged with one count of concealing a child-sex allegation, an allegation made against a priest, Jim Fletcher, in the 1970s.
Both men were working in the Maitland Diocese of New South Wales at the time, but they went on to meet very different fates.
In 2001, Philip Wilson was appointed Archbishop of Adelaide.
In 2006, Jim Fletcher died -- two years after being jailed for raping a 13-year-old boy between 1989 and 1991.
Nicky Davis is the leader of SNAP Australia, the Survivors Network of those Abused by Priests.
She says the charges demonstrate no-one is above the law.
"It's as big as the announcement of the royal commission, and it's what we've been waiting for. And it's what's desperately needed. At the end of the day, we need any official who is covering up child-sex crimes to be held accountable. If there is a conviction achieved, particularly if there's jail time served, this will be certainly an international precedent, and, hopefully, it will be a very strong message right through to the Vatican that Catholic Church officials are not above the law."
Archbishop Wilson is now the world's most senior Catholic clergyman to be charged with concealing a child-sex-abuse allegation.
He has denied the charge in a statement, saying he is taking immediate leave and has retained the services of one of Australia's top barristers.
"The suggestion appears to be that I failed to bring to the attention of police a conversation I'm alleged to have had in 1976, when I was a junior priest, that a now-deceased priest had abused a child."
"From the time this was first brought to my attention last year, I have completely denied the allegation."
A spokesman for the victim-support group Broken Rites Australia, Dr Bernard Barrett, says the case has worldwide significance.
And he suggests Archbishop Wilson should officially stand aside.
"It's merely a matter of standing aside and announcing, 'Somebody else will do my job for the time being until I return.' That would be more impressive to the public. Too often in the past, the Catholic Church has played down this problem of Church sexual abuse, and the cover-up all over Australia, all over the world, has gone on for so long. The public now needs to be assured that the Church is taking this seriously."
But Catholic commentator Paul Collins says the Church does take such matters seriously and Archbishop Wilson's reaction to the charge is the right one.
"Our legal adage is very, very clear: you're innocent until you're proven guilty. I think what Archbishop Wilson has done is correct. He's effectively stood aside from the government of the Archdiocese of Adelaide, and, as I understand it, he's also stood aside from membership of the committee that the Australian Bishops set up for Justice and Healing. There's is absolutely no doubt that, at the present moment, the Catholic Church takes all these allegations seriously and acts on them with greased lightning* in most cases. I don't think it throws any negative light on the Church's contemporary reaction."
The offence carries a potential sentence of up to two years in prison.
Archbishop Wilson has been issued with a notice to appear in the Newcastle Local Court on April the 30th.