According to the Scottish Daily Record, the incident happened outside of St Alphonsus' Church as people gathered for mass at the same time of an Orange Walk on Saturday.
A member of the church said the priest was spat on and hit with a baton as the Boyne parade passed by.
The worshipper told the paper: "The priest was spat at, verbally abused and also assaulted by a baton," he said.
"I was disgusted. "I eventually got hold of an officer after screaming at her to get resources to protect [him].
"[It was] little too late as the damage had already been done."
Police Scotland has not confirmed if a member of the parade is a suspect in the attack. However, a spokesperson conformed they were investigating the incident and there were no injuries.
Around 4,500 people took part in the Boyne parade through Glasgow City Centre.
