The Leaves of Time — Neal Barrett Jr.

The Gorgon came from some time line far across the multiple worlds. It moved among men, looking always as though it was one of them.

But it was not a man; it was a destroyer! This creature would willingly destroy the universe, in all its alternate world-lines. It could not tolerate other forms of life, could not permit them to exist.

The first a world knew of the beast in its midst was when its citizens began dying, horribly, and then it was already too late.