The "festival of dedication" (or "feast") in this verse was indeed the forerunner of what is today Hanukkah. It was established by Judas Maccabeus in the intertestamental period, as Jamieson, Fausset, and Brown write:
[This festival of the Dedication] was instituted by Jude Maccabeus, to commemorate the purification of the temple from the profanations to which it had been subjected by Antiochus Epiphanes 165 B.C., and kept for eight days, from the twenty-fifth Chisleu (December), the day on which Judas began the first joyous celebration of it (1 Maccabees 4:52,56,59; and Josephus, Antiquities, 7.7.7).
Now, the festival goes by the name Hanukkah, as Wikipedia indicates, but it is observed on the same day and celebrates the same event.
As to whether Jesus actually celebrated Hanukkah, that's a bit more controversial. John Wesley, following Grotius, thinks so:
So our Lord observed festivals even of human appointment. Is it not, at least, innocent for us to do the same? (source)
But Calvin suggests that his purpose was to further his ministry:
Christ appeared in the temple at that time, according to custom, that his preaching might yield more abundant fruit amidst a large assembly of men. (source)
So yes, this is a reference to Hanukkah, but it's harder to say if Jesus actually "celebrated" the holiday.