Archbishop of Adelaide Philip Wilson was convicted in May of covering up abuse by a paedophile priest, but has resisted calls to resign.
The most senior Catholic in the world to be convicted of the crime, Wilson has said he will appeal the verdict.
Mr Turnbull said: "The time has come for the Pope himself to sack him."
Two weeks after Wilson was sentenced to detention, the prime minister said that the "ultimate authority in the Church" must now intervene.
"There are many leaders that have called on him [Wilson] to resign - it is clear that he should resign," he told reporters in Sydney.
Throughout his trial, Wilson denied having known about the abuse of altar boys by a priest colleague, James Patrick Fletcher, in New South Wales in the 1970s.
But a court disagreed, with a judge saying that Wilson had remained silent in a bid to protect the Church's reputation.
Fletcher was convicted of nine child sexual abuse charges in 2004, and later died in jail.
Earlier this month, the Australian Catholic Bishops Conference said only the Pope had the authority to compel Wilson to resign.
Some bishops had "offered their advice privately", said Archbishop Mark Coleridge in a statement.
It came after a magistrate ordered Wilson to be assessed for a maximum 12-month sentence in "home detention" - meaning he is expected to avoid jail.
Wilson stepped aside from his duties after his conviction, but remains archbishop.
He said he would resign from his role if his appeal is unsuccessful.
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