St Mary's Catholic Church in Dandenong is the latest to suffer from what police are calling a suspicious fire.
The blaze started in the early hours of Tuesday, causing extensive damage.
On Monday fire almost destroyed the 123-year-old St James Church in Brighton, while a separate fire damaged St Mary's Church in St Kilda East.
The Dandenong church was one of eight Catholic churches linked to priest Kevin O'Donnell, who sexually abused children throughout his 50-year career in Melbourne parishes.
Local media have reported that in 1995 O'Donnell, aged 78, pleaded guilty to indecently assaulting 10 boys and two girls, aged between eight and 15, and spent 15 months in jail. He was freed in 1996 and died in 1997.
The other two churches were linked to paedophile priest Ronald Dennis Pickering, who served at various parishes in Melbourne between 1958 and 1993, before returning to his native Britain where he died in 2009.
In 2013, both men were on a list released by the Australian Catholic Church of 29 Melbourne priests who it acknowledged were guilty of sexually abusing children.
Police would not comment on the fires or any suspects other than to say they were all suspicious and were being investigated separately.
But Regional Bishop for the Catholic Church in Victoria Peter Elliott told Fairfax Radio he did not believe the fires were linked to anger over child sexual abuse, but were instead the work of a "very disturbed person".
The fires come as a Royal Commission into Institutional Child Sexual Abuse travels around Australia taking evidence about alleged child sex abuse linked to churches, charities and government agencies.
Local media have cited research by a Melbourne university that found at least five people had killed themselves after being sexually abused by Pickering between 1960 and 1980.
Hollywood actress and former St James' parishioner Rachel Griffiths said the church's destruction came as a relief because of its history.
"I was quite elated, like many of my generation, when I heard the news," she told the Australian Broadcasting Corporation.
"It's always been a difficult building for us to drive past because there's been so much tragedy and complicated feelings, I guess," she said.
Police in Victoria are investigating suspicious fires at three Melbourne churches where paedophile priests have served in the past.