John is not part of the Kingdom of Heaven because his role is to point to and prepare the way for it. Jesus is speaking in the language of eschatology and not in the framework of modern Christian theology.
The context of the passage is that John has been imprisoned by Herod:
Now when John heard in prison about the deeds of the Christ, he sent word by his disciples and said to him, “Are you the one who is to come, or shall we look for another?” And Jesus answered them, “Go and tell John what you hear and see: the blind receive their sight and the lame walk, lepers are cleansed and the deaf hear, and the dead are raised up, and the poor have good news preached to them. And blessed is the one who is not offended by me.”—Matthew 11:2-6 (ESV)
I think it would be natural for John to be worried about his legacy—he was about to be a martyr to an earthly authority and Jesus had not organized any resistance to that authority. In his distress, John sent his disciples for reassurance that Jesus is the Messiah the Israel was waiting for. Jesus' answer was to point to his work, which fulfilled prophecies such as Isaiah 29:17-24, which promised a restoration of the Kingdom of Israel after the Assyrian siege of Jerusalem.
Jesus then addresses the crowd about John's legacy. He contrasts John's poor attire and diet to that of someone living in a king's palace. People came to see John for the same reason they listened to Isaiah, Jeremiah, Elijah, and the rest of the great Biblical prophets: because he claimed to speak with God's voice against oppression and tyranny. John wasn't a draw because he brought God's blessing to the people, but because he was a messenger preparing the way.
With that in mind, we get to the passage in question:
Truly, I say to you, among those born of women there has arisen no one greater than John the Baptist. Yet the one who is least in the kingdom of heaven is greater than he. From the days of John the Baptist until now the kingdom of heaven has suffered violence, and the violent take it by force. For all the Prophets and the Law prophesied until John, and if you are willing to accept it, he is Elijah who is to come. He who has ears to hear, let him hear.—Matthew 11:11-15 (ESV)
There's a lot going on here and I can't address it all. However, the key analogy Jesus is drawing is between Herod/Herodias and Ahab/Jezebel (the violent who take the kingdom by force) and between John and Elijah (the ones who suffer violence, but are eventually vindicated). In other words, we should not be surprised John suffered under the thumb of a false king, since all the prophets suffered the same fate.
This analogy is immediately followed by Jesus comparing the people to fickle children. They complained because:
- John was too much of an ascetic, and
- Jesus was too worldly.
But this misses the broad sweep of Israel's history. Jesus saw himself as the master of the messianic banquet, which was anticipated in Jewish eschatology at the time. Those who are downtrodden in the oppressive kingdoms of earthly rulers will rejoice in a reversal of fortunes in the kingdom of heaven. Jesus illustrates the sea change (into something rich and strange) by contrasting the greatest outside of the kingdom to the least in it. At that moment, John certainly was not in the kingdom since he was a forerunner to it and was a prisoner of the violent powers.
Later in the same address, Jesus says:
Come to me, all who labor and are heavy laden, and I will give you rest. Take my yoke upon you, and learn from me, for I am gentle and lowly in heart, and you will find rest for your souls. For my yoke is easy, and my burden is light.—Matthew 11:28-30 (ESV)
This invitation is open to all people, including John the Baptist. Remember in the beginning of the passage, John expressed doubt that Jesus was who he said he was. Jesus' answer boils down to, "Trust me. It's all going to turn out ok." John the Baptist did die, but the message of Matthew (and the other gospels) is that Jesus overcame the power of death in his own death and resurrection.