From the MM
Damage Reduction (Ex or Su): A creature with this special quality ignores damage from most weapons and natural attacks.
So it's either Extraordinary or Supernatural. However, for example a Satyr which has Damage Reduction 5/cold iron, it doesn't mention if this is Ex or Su.
However the DMG says:
The arrow sticks into the vampire, but she just pulls it out and laughs as the wound instantly heals. “You’ll need to do better than that,” she hisses.
Some magic creatures have the supernatural ability to instantly heal damage from weapons or to ignore blows altogether as though they were invulnerable.
Where it says it's a supernatural ability. However; I would assume that it wouldn't always be supernatural, like in the case of a naturally thick hide or some sort of amazing healing ability (like Wolverine). Am I to read this that only magical creatures have it as a supernatural ability and others are extraordinary abilities?
Generally only interested in an answer according to published rulebooks.