*[Cruel][1]* is possibly the most often used adjective for this context, though from my experience *cruelty* (as a noun) is more common.  (E.g. [SPCA][2] stands for the Society for the Prevention of Cruelty to Animals.)  The Wikipedia article is called *[Cruelty to animals][3]* and says that it is also called *animal abuse* or *animal neglect*.

Unfortunately there appears to be no word used exclusively for animals, not for people.

It's worth noting that even if the word *inhumane* is not commonly used to describe cruelty to animals, *humane* appears to be most often used as its antonym, as in the *[Humane League][4]*, *[Humane Society][5]*, or *[humane treatment][6]*.


  [1]: http://dictionary.reference.com/browse/cruel
  [2]: http://en.wikipedia.org/wiki/Society_for_the_Prevention_of_Cruelty_to_Animals
  [3]: http://en.wikipedia.org/wiki/Cruelty_to_animals
  [4]: http://www.thehumaneleague.com/
  [5]: http://www.humanesociety.org/
  [6]: http://www.google.com/search?gcx=c&sourceid=chrome&ie=UTF-8&q=humane%20treatment