Upvote:10
By "Syria" in this passage, the evangelist did not intend specifically the area now taken up into the Arab Republic of Syria (which was not a country until after the First World War). Rather, what was meant was the Roman province of Syria, which included all the modern-day country of Lebanon, as well as parts of modern-day Israel, Jordan, and Syria. It was a much larger area than the Roman client kingdoms of Judea or Galilee (which it included), and there were Jews throughout the area at that point.
In other words, as the evangelist is using "Syria" here, Jesus was already in Syria - he was born, lived, and died in Rome's Syria Provincia. The impression the evangelist wants to give is of Jesus' reputation spreading over a much wider area than just the neighborhood he was traveling and working in at the time.