I never really noticed this before but it does seem odd that everyone is to be baptized in the name of the Father, Son and Holy Spirit, yet it does not appear that the Apostles were. At least there is no event of their baptism recorded in scripture. Is there any early explanation of why from church Fathers?
Tertullian comments on this issue, at some length. I confess, I don't quite understand what he is saying---if indeed he is saying anything or just blathering on aimlessly---but I will quote him entirely (source):
When, however, the prescript is laid down that “without baptism, salvation is attainable by none” (chiefly on the ground of that declaration of the Lord, who says, “Unless one be born of water, he hath not life”), there arise immediately scrupulous, nay rather audacious, doubts on the part of some, “how, in accordance with that prescript, salvation is attainable by the apostles, whom—Paul excepted—we do not find baptized in the Lord? Nay, since Paul is the only one of them who has put on the garment of Christ’s baptism, either the peril of all the others who lack the water of Christ is prejudged, that the prescript may be maintained, or else the prescript is rescinded if salvation has been ordained even for the unbaptized.” I have heard—the Lord is my witness—doubts of that kind: that none may imagine me so abandoned as to excogitate, unprovoked, in the licence of my pen, ideas which would inspire others with scruple. And now, as far as I shall be able, I will reply to them who affirm “that the apostles were unbaptized.” For if they had undergone the human baptism of John, and were longing for that of the Lord, then since the Lord Himself had defined baptism to be one; (saying to Peter, who was desirous of being thoroughly bathed, “He who hath once bathed hath no necessity to wash a second time;” which, of course, He would not have said at all to one not baptized;) even here we have a conspicuous proof against those who, in order to destroy the sacrament of water, deprive the apostles even of John’s baptism. Can it seem credible that “the way of the Lord,” that is, the baptism of John, had not then been “prepared” in those persons who were being destined to open the way of the Lord throughout the whole world? The Lord Himself, though no “repentance” was due from Him, was baptized: was baptism not necessary for sinners? As for the fact, then, that “others were not baptized”—they, however, were not companions of Christ, but enemies of the faith, doctors of the law and Pharisees. From which fact is gathered an additional suggestion, that, since the opposers of the Lord refused to be baptized, they who followed the Lord were baptized, and were not like-minded with their own rivals: especially when, if there were any one to whom they clave, the Lord had exalted John above him (by the testimony) saying, “Among them who are born of women there is none greater than John the Baptist.” Others make the suggestion (forced enough, clearly “that the apostles then served the turn of baptism when in their little ship, were sprinkled and covered with the waves: that Peter himself also was immersed enough when he walked on the sea.” It is, however, as I think, one thing to be sprinkled or intercepted by the violence of the sea; another thing to be baptized in obedience to the discipline of religion. But that little ship did present a figure of the Church, in that she is disquieted “in the sea,” that is, in the world, “by the waves,” that is, by persecutions and temptations; the Lord, through patience, sleeping as it were, until, roused in their last extremities by the prayers of the saints, He checks the world, and restores tranquillity to His own. Now, whether they were baptized in any manner whatever, or whether they continued unbathed to the end—so that even that saying of the Lord touching the “one bath” does, under the person of Peter, merely regard us—still, to determine concerning the salvation of the apostles is audacious enough, because on them the prerogative even of first choice, and thereafter of undivided intimacy, might be able to confer the compendious grace of baptism, seeing they (I think) followed Him who was wont to promise salvation to every believer. “Thy faith,” He would say, “hath saved thee;” and, “Thy sins shall be remitted thee,” on thy believing, of course, albeit thou be not yet baptized. If that was wanting to the apostles, I know not in the faith of what things it was, that, roused by one word of the Lord, one left the toll-booth behind for ever; another deserted father and ship, and the craft by which he gained his living; a third, who disdained his father’s obsequies, fulfilled, before he heard it, that highest precept of the Lord, “He who prefers father or mother to me, is not worthy of me.”
Aquinas is much clearer. He simply believed that John the Baptist's baptism was sufficient. He wrote (source):
Further, the apostles were baptized with John's baptism, since some of them were his disciples, as is clear from Jn. 1:37. But the apostles do not seem to have been baptized with the baptism of Christ: for it is written (Jn. 4:2) that 'Jesus did not baptize, but His disciples.' Therefore it seems that those who had been baptized with John's baptism had not to be baptized with the baptism of Christ.
You can continue to sift through the earliest sources by searching Google using this site on the Ante-Nicene Fathers. A similar search on Augustine might be helpful also.
Anonymous answered your question because these quotes are from early church fathers, describing their thoughts as to whether or not the apostles were baptized. I would like to add a few points, mainly to clarify the difference between Tertullian and Aquinas, but also to question the (common) premise that the New Testament doesn't record the baptism of the apostles. I think the premise is partially inaccurate. There are, essentially, two types of baptism recorded in the NT. While it's true that the NT does not clearly record a "manmade" water baptism of the apostles, I think it does record the apostles being baptized by The Holy Spirit. Because that baptism is spiritual, it's not going to be clear in the text. But I think it's there, in clues.
I think these clues are hiding underneath your question. In other words, what does it mean to be baptized "in the name of The Father, Son and Holy Spirit?" Does it mean that a priest or a pastor simply says, "in the name of..." or does "the name" mean something else? I would argue that it means something else. "The Name" ("Ha Shem") is literally used over 7,000 times in the tanach. This would be a good separate question so I'll pose this here and continue.
Tertullian & Aquinas
Tertullian spends most of his time explaining how "audacious" people are, suggesting that the apostles never received a baptism by Christ. He goes back and forth about what others are saying regarding the necessity of baptism. It isn't until his last few sentences that Tertullian says -regardless of whether or not they were baptized- they accomplished the "highest precept" -they left their parents for him. And so, he remembers what Christ said :
"Thy faith, [Christ] would say, has saved thee." (compare to Luke 7:50)
And yet, Tertullian is directing this type of faith toward salvation, so he is speaking of the faith the apostles had prior to Christ's death and this was a much weaker faith. The faith the apostles had once they knew Christ resurrected was a much more powerful faith.
Aquinas is not speaking of the baptism of The Holy Spirit that comes only through the resurrection of Christ. He's speaking of the "water baptism" that was prevalent in that society at the time. Two separate baptisms. And Christ refused to baptize in this way.
John 4:1-2, Codex Sinaiticus (translated from: www.codexsinaiticus.org)
"When therefore Jesus knew that the Pharisees had heard that Jesus was making and baptizing more disciples than John, though Jesus himself baptized not, but his disciples baptized."
So Tertullian recognizes the key ingredient to the more significant baptism -faith- though it isn't clear whether or not he thought this was acquired through water baptism. Aquinas, on the other hand, acknowledges water baptism and assumes that John's baptism has the mark of salvation, but this is nowhere in the text.
Does the NT fail to record the baptism of the apostles?
John 20:22, Textus Receptus
καὶ τοῦτο εἰπὼν ἐνεφύσησεν καὶ λέγει αὐτοῖς Λάβετε πνεῦμα ἅγιον
John 20:22, Codex Sinaiticus; translated from: codexsinaiticus.org
"And having said this, he breathed on them and said to them: Receive the Holy Spirit."
The word in bold is "emphysao." It is not the "pneuma" often used in Greek. "Emphysao" is used once in the New Testament and at Genesis 2:7 (LXX). This is significant. In Genesis 2:7, Adam is created through the breath (Septuagint, "emphysao") of God. Here, Christ -The Son- is giving this same "emphysao" breath from The Father (Genesis 2:7) to the new creation. This is The Holy Spirit. Scholars call this the "Johannine Pentecost."
Acts 2:37, Codex Sinaiticus; translated from: codexsinaiticus.org
"And Peter said to them: Repent, and be baptized every one of you in the name of Jesus Christ, for remission of your sins, and you shall receive the gift of the Holy Spirit."
Peter says this after the incident at Pentecost where "all of them were filled with The Holy Spirit" (Acts 2:1-4). Peter is referring to The Holy Spirit. Because this happened directly after the resurrection of Christ, this "fill[ing]" came from Christ, the Son. The father is involved because it is the same breath/spirit as in Genesis 2:7. The son had to come from the father.
"No one comes to the Father except through me." (John 14:6, NET)