In the Philip K. Dick short story The Variable Man
, Earth is at war with the Centaurian Empire (which in the story completely circles our solar system). Earth scientists invent a missile that will fly toward Centaurus at FTL speeds, and then drop out of FTL inside the star. Due to the method of FTL, dropping out of FTL speeds means that the object has nearly infinite mass at relativistic speeds, which would cause the sun to implode.
It's not "warp", but it is FTL. When traveling at near FTL speeds, according to relativity the object will have nearly infinite mass. That would be the cause of any damage. Warp bubbles work differently, though, in that the mass of the object at warp is actually decreased.