The Cyprus Mail has reported that the conflict began after the best man was pushed in a light-hearted way during a special Isaiah Dance - where guests circle the alter three times.
Reports from the day suggest an unnamed priest and family members became involved in a brawl.
The Mirror has suggested the priest put down his prayer book and punched the groom's brother in the face.
The man was left bleeding after the alleged incident.
After the fight, the wedding ceremony continued on as usual and the priest fled the church.
The couple are now looking to file a complaint.
