No. John the Baptist was in prison and he sent his disicples to Jesus to ask, "Are you the One who is to Come?" and Jesus sent his reply, "Tell John that The blind see, the deaf hear, the lame leap for joy, and the acceptable year of the Lord's favour is proclaimed".
Jesus did not kill John the Baptist. Herod did the deed.
According to Mark's gospel Herodias bore a grudge against John for stating that Herod's marriage to Herodias was unlawful; Herodias encouraged Salome to demand that John be executed.
And when a convenient day was come, that Herod on his birthday made a supper to his lords, high captains, and chief estates of Galilee; And when the daughter of the said Herodias came in, and danced, and pleased Herod and them that sat with him, the king said unto the damsel, Ask of me whatsoever thou wilt, and I will give it thee. And he sware unto her, Whatsoever thou shalt ask of me, I will give it thee, unto the half of my kingdom. And she went forth, and said unto her mother, What shall I ask? And she said, The head of John the Baptist.