Canon 44 of the so-called Fourth of Carthage, which in reality represents the synodal decrees of some council in Southern Gaul in the time of St. Cæsarius of Arles (c. 503). There it enjoined that a cleric is to allow neither hair nor beard to grow freely (Clericus nec comam nutriat nec barbam) though this prohibition is very probably directed only against beards of excessive length. Still this canon, which was widely quoted and is included in the "Corpus juris" had great influence in creating a precedent.
This wasn't canon law as far as I can see --
Of course, priests in the Byzantine church are generally required to wear beards, and at least one religious order in the West also required beards.