There’s no direct mention of the White Walkers or the army of the dead anywhere in the Azor Ahai prophecy, but there is another prophecy (two things are for certain in fantasy writing: prophecies and giant spiders). In both the first book and first season, Old Nan mentioned the long night when the Walkers first came. In the book, though, the story is longer. The book also makes reference to the Last Hero, the one who fought the Walkers.
Later, in the fourth book, A Feast for Crows, Sam tells Jon about an account he read concerning the long night, which mentioned the Last Hero. It states that the Last Hero fought the White Walkers with something called dragonsteel. In the show, we see Jon defeat a White Walker with Longclaw, his Valyrian steel sword.