There is no mention either of the holiday of Hanukkah, nor of the historical events that led to its establishment, in the Bible.
The most detailed account of the story of Hanukkah is contained in the First and Second Books of Maccabees. However, these books are not included in the Hebrew Bible.
The Books of Maccabees are part of what are known as the Apocrypha (Greek for “hidden things”), which was considered part of the biblical canon by the Jews of Alexandria, but not by the Jews in ancient Israel.
It is not clear exactly why these books were excluded, though there are several theories — none of them completely satisfying. One is that the ancient rabbis who established the biblical canon preferred older works, and Maccabees is comparatively new (though just as new as the Book of Daniel, which is included). Others have suggested the exclusion was the result of ancient Jewish rivalries or due to the practical desire not to promote the story of an earlier successful Jewish rebellion at a time when the Jews had recently failed in their revolt against the Romans.
The holiday of Hanukkah only appears in later Jewish texts, specifically the Talmud, where the earliest details of the practice of the holiday and the kindling of lights are contained.