A magistrate last month ordered former Adelaide Archbishop Philip Wilson to be detained at his sister's house in New South Wales state for at least six months of a one-year sentence before he is eligible for parole.
The 67-year-old cleric was convicted in May of failing to report to police the repeated abuse of two altar boys by a paedophile priest in the Hunter Valley region north of Sydney during the 1970s.
The Australian director of public prosecutions' office said prosecutors are appealing the "inadequacy" of the sentence in the New South Wales District Court.
Wilson had faced a possible sentence of up to two years in prison.
He will appeal his conviction in the District Court in a hearing in November, Australian Broadcasting Corp reported.
Wilson denied the accusations and had refused to resign pending an appeal. However, Pope Francis accepted Wilson's resignation in July after pressure mounted, including from Australia's prime minister, for him to be fired.
He had failed four times to have courts throw out the charge since he was first indicted in 2015.
Wilson temporarily stepped down as Adelaide archbishop after he was convicted in May. Adelaide is the capital of South Australia state, which will bring in laws in October obliging priests to report evidence of abuse heard during a confession.
The Australian Capital Territory and Tasmania state are planning similar laws.
Wilson was once Australia's highest-ranking bishop as president of the Australian Catholic Bishops' Conference.
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