Does Christianity claim that the Bible is God's only Word? If yes, what is the reference for this?

By this logic, any book before the Bible like the Torah is not the word of God.

According to Islam, Torah is the book of prophet Moses and Bible is the book of prophet Jesus and Quran is the book of prophet Muhammad.
The assumption that you make is that the Bible is "Jesus' book." It may or may not be the "Injil." In fact, Jesus neither wrote nor actually authored any piece of the book. Indeed, unlike Muhammed, Jesus did not even receive the Word, but rather was the Word of God.  As John 1 tells us:


  1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was with God in the beginning. 3 Through him all things were made; without him nothing was made that has been made. 4 In him was life, and that life was the light of all mankind.  ... 14 The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.


This is picked up in Hebrews, where the author states:


  1 In the past God spoke to our ancestors through the prophets at many times and in various ways, 2 but in these last days he has spoken to us by his Son, whom he appointed heir of all things, and through whom also he made the universe. 


Indeed, while the Bible is our perfect guide to the nature of God, it is to be understood that the Word points us to God because God is holy. 

That Jesus is the exclusive way of salvation is made clear by Jesus' first disciples, Peter and John.  When the Jewish High Priest brought them up on charges, they said of Jesus:


  Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved. (Acts 4:12)


Furthermore, Jesus himself was clear that he was the exclusive one and only Word, saying in John 14:6:


  Jesus answered, "I am the Way and the Truth and the Life. No one comes to the Father except through me.


The fundamental distinction I am making is this - Christians do not believe Jesus to be a prophet or a teacher. Christians believe him to be God. As God, he was "the Word" (a Greek term Logos that brings the fundamental idea of being the one through whom all things are created and given meaning.) Muhammed did not claim to be God. Jesus did. The exclusivity of the "Bible" as God's Word doesn't make sense, because Jesus is the point, not the book. Unlike Islam, we do not restrict our understanding of God's Word to a single language, nor do we venerate the Scriptures as Islam does. Instead, we believe that God is "the Word" and that Jesus is God, not a prophet

The Bible (and I say this as one who has an exceedingly high view of the authority of Scripture!) is not the "ONLY" word of God, because Jesus is the Word. Any would-be Scripture that denies this fundamental tenet of who Jesus is, is by definition, not a Christian Scripture. Jesus, being the fundamental Word, is the only test.

Unlike a prophet who merely is God's servant, as Christians, we make the audacious claim that God became flesh, dwelt among us, loved us, and saved us.  Jesus is not a messenger, but God.