This is a teaching of the Catholic Church. Since our bodies are temples of the Holy Spirit, Jesus Christ (who is Divine as well as human) would not have been born into this world by way of an unclean temple. This is why the Church teaches Mary was without original sin.
While the Bible contains the written Word of God, the Word of God also lives in the Church. (Jesus established the Church and promised that evil shall never overcome it - therefore what the Church teaches is the Word of God even if it's not in the Bible)
There are many things that are not in the Bible, but are nonetheless just as true as if they were. This is very evident in the last verses of John's Gospel.