No, you don't.

Because it is functioning as a title introduction to what follows the colon. Similar to a book titled "Apples and Pears", we don't need to write "(The) Apples and (The) Pears". You would need "the" if you wrote it out this way: The translation is as follows, "The apple doesn't fall far from the tree". An English major could explain it better but that's the gist.