Cruel is possibly the most often used adjective for this context, though from my experience cruelty (as a noun) is more common. (E.g. SPCA stands for the Society for the Prevention of Cruelty to Animals.) The Wikipedia article is called Cruelty to animals 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, Humane Society, or humane treatment.