Gregory of Nazianzus

The birth of John then broke the silence of Zacharias, as it follows, And his mouth was opened. For it were unreasonable when the voice of the Word had come forth, that his father should remain speechless.

Catena Aurea by Aquinas ↗

Theophylact of Ohrid

John means "the grace of God"; therefore the father also immediately received grace and prophesies first about Christ, and then also about his son.

Commentary on Luke ↗

Ambrose of Milan

Rightly also, from that moment was his tongue loosed, for that which unbelief had bound, faith set free. Let us then also believe, in order that our tongue, which has been bound by the chains of unbelief, may be loosed by the voice of reason. Let us write mysteries by the Spirit if we wish to speak. Let us write the forerunner of Christ, not on tables of stone, but on the fleshly tablets of the heart. For he who names John, prophesies Christ. For it follows, And he spake, giving thanks.

Catena Aurea by Aquinas ↗

Bede

His mouth and his tongue were immediately opened, and he spoke, blessing God. And fear came upon all their neighbors. Because the voice of one crying in the wilderness was born, rightly was the father's tongue loosened. For it was not fitting that the father remain silent from praises, who rejoiced in the birth of the herald of the Word. Indeed, the lips bound by unbelief were now loosened by faith. …

On the Gospel of Luke ↗

Bonaventure

And immediately his mouth was opened, etc. After the birth from the barren woman and the circumcision and the naming of the infant, there follows the opening of the priestly mouth, according to the word of the heavenly messenger. This miracle was demonstrative of the prerogative and excellent magnificence in John, so that it might deservedly be shown that he is called by this name. In the description of this miracle, three things are intimated, namely, the evidence of the miracle, and its reverence, and the understanding of the same. …

Commentary on Luke, Chapter 1 ↗