The assault was described as "callous and cowardly" by police, who are appealing for witnesses to come forward.
The victim had just collected his winnings from a bookmakers on Saturday night and was walking through the car park of the Immaculate Conception Chapel in Glasgow's Maryhill Road.
A man grabbed him, dragged him to the ground, punched him and stole his wallet. The suspect then walked from the scene along Maryhill Road at about 6:20pm.
Detective Constable Alex Cameron said: "This was an extremely callous and cowardly attack on a vulnerable man who had no chance against the suspect.
"The victim is an ex-soldier who has fought for his country, and to be dragged to the ground and robbed on his way to Mass is deplorable.
"He is also hard of hearing and would have been caught completely unaware. Thankfully, he hasn't been injured, however he is naturally suffering from shock."
Detectives have been speaking to parishioners who were also attending the church service, checking with local shopkeepers and reviewing CCTV from around the area.
DC Cameron added: "The victim had been in nearby William Hill bookmakers prior to the attack to collect a small winning. Therefore the suspect may have witnessed this and followed him to the Chapel.
"We will be looking at available CCTV from the bookmakers, but would ask anyone who was in William Hills at 1957 Maryhill Road and who perhaps saw the suspect there to contact us.
"I also appeal to anyone who was in the area of the Immaculate Conception Chapel and who saw anything at all to come forward. It is imperative we trace this man."
The suspect is described as a white male, aged 35 to 40, about 5ft 4in tall, of slim build and gaunt appearance.