Judea to Galilee--Section 26, Subdivision A

Section 26
JESUS SETS OUT FROM JUDEA FOR GALILEE
Subdivision A
REASONS FOR RETIRING TO GALILEE
A. MATT. 4:12
B. MARK 1:14
C. LUKE 3:19, 20
D. JOHN 4:1- 4

 Mat 4:12  When Jesus heard that John had been arrested, He left Judea and returned to Galilee. 

Source: Generation Word

The Judean ministry of Jesus, which lasted almost one year, is not discussed by Matthew. This one year period is covered in John 1-4 and fits between Mat_4:11 and Mat_4:12. Matthew takes us from the temptation directly to the Galilean ministry.-BKC

But it was not fear that drove Him north to Galilee. Actually He was going right into the center of Herod's kingdom—the same king who had just imprisoned John. In moving to Galilee of the Gentiles, He was showing that His rejection by the Jews would result in the gospel going out to the Gentiles.-BB

Mar 1:14  Later on, after John was arrested, Jesus went into Galilee, where He preached God's Good News.

Luk 3:19-20  John also publicly criticized Herod Antipas, the ruler of Galilee, for marrying Herodias, his brother's wife, and for many other wrongs he had done. So Herod put John in prison, adding this sin to his many others.

Scholars debate the dates of John the Baptist’s imprisonment and death. It is likely that John began his ministry about a.d. 29 (cf. Luk_3:1), that he was imprisoned the following year, and that he was beheaded not later than a.d. 32. His entire ministry lasted no more than three years - about one year out of prison and two years in prison. -BKC

Joh 4:1-4
  Jesus knew the Pharisees had heard that He was baptizing and making more disciples than John  (though Jesus Himself didn't baptize them—His disciples did). So He left Judea and returned to Galilee.  He had to go through Samaria on the way.

4:3 By leaving Judea and journeying to Galilee, Jesus would prevent the Pharisees from being successful in their efforts to cause divisions. But there is something else of significance in this verse. Judea was the headquarters of the Jewish religious establishment, whereas Galilee was known as a heavily Gentile region. The Lord Jesus realized that the Jewish leaders were already rejecting Him and His testimony, and so here He turns to the Gentile people with the message of salvation.-BB

From Fourfold Gospel, another explanation:

We have in these verses two reasons assigned for the withdrawal of Jesus into Galilee, namely: 1. The imprisonment of John the Baptist [139] 2. Knowledge of the Pharisees that Jesus was baptizing more disciples than John. The first gives us the reason why he went to Galilee, the second the reason why he left Judea. Jesus did not go into Galilee through fear of Herod, for Herod was tetrarch of Galilee. The truth is, the absence of John called for the presence of Jesus. The northern part of Palestine was the most fruitful soil for the gospel. During the last six or eight months of John's ministry we find him in this northern field, preparing it for Christ's kingdom. While we can not say definitely that John was in Galilee (Bethabara and Ænon being the only two geographical names given), yet he certainly drew his audiences largely from the towns and cities of Galilee. While John occupied the northern, Jesus worked in the southern district of Palestine; but when John was removed, then Jesus turned northward, that he might sow the seed of the kingdom in its most fruitful soil. But if there was a reason why he should go to Galilee, there was an equal reason why he should depart from Judea. His popularity, manifesting itself in the number of his baptisms, was exciting that envy and opposition which caused the rulers of Judea eventually to take the life of Jesus (Matt.27:18).