The first mention is very early, in the Confiteor which is prayed twice, once by the priest and once by the server.
Confíteor Deo omnipoténti, beátæ Maríæ semper Vírgini, beáto Michaéli Archángelo, beáto Joanni Baptístæ.... Ideo precor beátam Maríam semper Vírginem, beátum Michaélem Archángelum, beátum Joánnem Baptístam, &c.That adds up to four invocations of John by name before the Introit.
The Gloria refers to Christ as the Agnus Dei, the Lamb of God, as he was named by the Baptist.
After the washing of hands, in the Suscipe, sancta Trinitas, John is mentioned by name after the Virgin and before Peter and Paul.
In the canon, the Communicantes omits the Baptist, including rather John the Apostle and the John who was martyred under Julian the Apostate.
After the consecration, the Nobis quoque peccatoribus invokes the martyrs, with the Baptist at the head of the list.
The thrice-hymned Agnus Dei of course reflects the proclamation of the Forerunner of the identity of the Christ.
Before the people's communion, the celebrant declares: Ecce Agnus Dei, ecce qui tollit peccáta mundi. This quotes the Baptist again more fully regarding the Christ (cf. Jn 1.29).
Finally, the Last Gospel makes reference to the witness of John as one giving testimony of the Light.
The testimony of St. John the Baptist is so important to the liturgy of the Mass that the priest not only prays to, but with, him multiple times. Traditionally in the Roman Rite, the feasts of the Baptist were of the greatest importance after the feasts of Christ, the Virgin, and the Angels. This is reflected mightily in the Mass itself.
"Such an one was John, who regarded not the multitude, nor opinion, nor anything else belonging to men, but trod all this beneath his feet, and proclaimed to all with becoming freedom the things respecting Christ. And therefore the Evangelist marks the very place, to show the boldness of the loud-voiced herald. For it was not in a house, not in a corner, not in the wilderness, but in the midst of the multitude." —St. John Chrysostom