From Bart Ehrman’s Lost Gospel of Judas Iscariot:

For I received from the Lord that which I also handed over to you, that the Lord Jesus, on the night in which he was betrayed, took bread, and after giving thanks, broke it and said, “This is my body given for you.” (1 Cor. 11:23–24) The key phrase for us, of course, is the statement that this took place “on the night in which he was betrayed.” Surely this is a reference to the betrayal of Jesus by Judas Iscariot, so even though the betrayer is not mentioned by name, it is clear that Paul knows all about the incident.

But in fact the matter is not so clear. The problem has to do with the Greek word that Paul uses when he says that Jesus was “betrayed” (Paul, and all the other authors of the New Testament, wrote in Greek). The word is common in the New Testament—Paul himself uses it over fifteen times in his letters, including one other time in the passage I just quoted. When Paul says that the information he is now relating is what he also “handed over” to the Corinthians, it is the same word he uses when he indicates that Jesus was “betrayed.” The Greek word is paradidomi—and it literally means “to give or hand someone or something over to someone else.”

Is Paul referring, then, to Judas Iscariot handing Jesus over to the ruling authorities for trial? Probably not, for in every other instance that Paul uses paradidomi with reference to Jesus, it refers to the act of God, who “handed Jesus over” to death for the sake of others. This can be seen, to choose just one passage, from Romans 8:32:

What then shall we say to these things? If God is for us, who is against us? He who did not spare his own son, but handed him over [paradidomi] for all of us—how will he not give us all things with him?

Since Paul doesn’t specify that he is talking about the betrayal of Jesus by Judas in 1 Corinthians 11:23–24, the translation I gave of the passage may be inaccurate. Probably it would be better to stick with how Paul uses the word in question elsewhere, and translate it as follows:

For I received from the Lord that which I also handed over to you, that the Lord Jesus, on the night in which he was handed over [by God, to face death], took bread, and after giving thanks, broke it and said, “This is my body given for you.” (1 Cor. 11:23–24)

If this translation is correct, then there is no reference in any of Paul’s letters to Judas Iscariot or to his act of betrayal. In fact, there is one passage that might suggest that Paul did not know about Judas and his betrayal. Later in the same book, Paul is discussing the appearances of Jesus to various groups and individuals after his resurrection (1 Cor. 15:3–8), and here he states that “[Christ first] appeared to Cephas, and then to the Twelve.” This clearly refers to Jesus’ twelve disciples, but how could he have appeared to all of them if Judas was no longer among their number? Either Paul is using the term “the Twelve” as a shorthand reference to Jesus’ closest disciples—so he doesn’t really mean there were exactly twelve of them—or he doesn’t know the tradition that one of the Twelve had betrayed his master and departed from the group.