They began to argue and the man allegedly produced a kitchen knife from his trousers and stabbed Rev Mathew in the neck in front of dozens of parishioners.
The priest was due to give the 11am Italian-language mass on Sunday.
"You can imagine our shock", said one long-time volunteer at the parish, located in William St in Fawkner, in Melbourne's northern suburbs.
"But the ambulance was here quickly and he just walked out to get into the ambulance". The man entered the church and confronted the priest in the foyer.
A 72-year-old man from Fawkner was arrested and charged with intentionally and recklessly causing injury.
A woman, who didn't want to be identified, said there were chaotic scenes when the stabbing happened.
Devotees said the assailant was a frequent visitor to the church.
Melina, a parishioner who witnessed the incident There was some shouting and a lot of movement at the back of the church and then I saw Father Tommy coming to approach me. "As I removed some of his garment I could see quite a bit of blood".
"Fr Tomy would like to say that he is recovering well and is in good spirits".
They began to argue and the man produced a kitchen knife from his trousers and stabbed Father Mathew in the neck in front of dozens of parishioners.
The police are yet to confirm if it is a case of racist abuse.
According to the news report, it is believed that the offender told the priest that because he was an Indian, he must be a Hindu or a Muslim and therefore can't be saying mass.