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According to Catholicism, by whom was John the Baptist was baptized?
The Church teaches nothing on this matter. Nor is there even a tradition of the possibility that he was baptized.
To say otherwise is pure speculation!
Although SLM’s answer seems to allude to such a possibility, it is still speculation and no sources of concrete historical evidence exist that state that St. John the Baptist was indeed baptized.
Several holy fathers write that Elizabeth fled with her child into the desert, to conceal herself from the cruelties of king Herod; and that John was nourished and kept either by an angel or in some other manner by divine Providence. Others write that, in his third or at most in his fifth year, he had voluntarily gone into the desert, eager to serve God more perfectly and to prepare himself for his mission. No one ought to think this incredible; since, even before he was born, he was gifted with the use of his reason, and comprehended the great mission to which he was called by the Almighty. So much is certain that he was from his most tender years in the wilderness. The holy Evangelists and the holy fathers tell us what manner of life he led there. He subsisted on wild honey and locusts, which are used as food in the East; but he ate so little, that our Lord said of him, that he had neither taken food nor drink. His drink was water; his garments, a coat of camels'-hair, which was fastened round his loins by a leathern belt. The ground was his bed, and he employed day and night in prayer and meditation. By fasting and other austere penances, he prepared himself for his mission. St. Augustine remarks that the severe life of penance of John was the model after which the hermits regulated their lives; hence they acknowledge him as their founder.
When in his thirtieth year, St. John was admonished by God to leave the wilderness and commence his mission. Going to the river Jordan, he preached penance and baptized the penitents. This baptism was not that which Christ instituted in the course of time: neither had it the power which the baptism of Christ has; but was only a sign of penance. In the Gospel it is related how great a multitude of people came to St. John; what he preached; how he exhorted them to do penance: how he had the honor to baptize Christ Himself, and what occurred during this event. The splendid testimony is spoken of, which he gave at different times, to the effect that Christ was the true Messiah. It is also recorded what he answered to those who were sent to him to ask whether he was the promised Messiah; for, his life was so holy and wonderful, that many believed him to be the long promised Redeemer. The Nativity of St. John, the Baptist
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Traditionally, it is understood that John the Baptist was free from original sin from his Mother's Womb:
and he shall be filled with the Holy Ghost, even from his mother's womb. (Luke 1:15)
and his leaping for joy in Elizabeth's womb when Mary arrived is understood as the sign of the Holy Spirit indwelling within him. Being free from original sin from before birth removes any further need to be baptized. Incidentally, this is also why he and Mary are the only ones besides Christ to have birthdays celebrated in the liturgical year.
See St John the Baptist in the Catholic Encyclopedia for further information.
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Although not a strictly Catholic Church point of view, by making the OP association between baptism and tvilah, we can find an answer to the question who baptized John?
John the baptist's father was Zachariah. According to the bible, he was of the Levitical priestly tribe.
There was in the days of Herod, the king of Judaea, a certain priest named Zacharias, of the course of Abia: and his wife was of the daughters of Aaron, and her name was Elisabeth. Luke 1:5
The "course of Abia" was the eighth course of a number of 24 priests appointed to serve in the temple.
These were the orderings of them in their service to come into the house of the LORD, according to their manner, under Aaron their father, as the LORD God of Israel had commanded him. 1 Chron 24:19
Zachariah was in the temple when the angel announced he would have a son to be named John.
But the angel said unto him, Fear not, Zacharias: for thy prayer is heard; and thy wife Elisabeth shall bear thee a son, and thou shalt call his name John. Luke 1:13
A priest begins to serve at the age of thirty. He is washed.
Then bring Aaron and his sons to the entrance to the tent of meeting and wash them with water. Ex 29:4
Though we do not find an explicit reference that John had been washed/baptized for his Levitical service, it is implied like all other sons of Aaron who served.
Though some may say there's also no proof John served in the temple, the explanation would lie in the similarity to when Moses first consecrated Aaron into the priestly service, though Moses was not a priest per se. (Ex 29).