An unknown male gained entry to the parish on Barkley Street, Ararat, at about 11pm on Wednesday, July 17.
Police were told he got in through a bedroom window, before he woke up a sleeping priest.
The man demanded money, and fled the scene with about $1000 from the parish safe.
The priest was not physically injured.
Police have released images of a male they believe may be able to assist with their enquiries.
He is described as being of slim to medium build and was wearing a dark hooded jumper and pants.
