In general, the laws of kosher are for (Jewish) humans, not for animals.

There are, however, two sorts of non-kosher food that we are not only forbidden to eat, but we are also forbidden to derive any benefit from:

1) Chametz on Passover. (Click here for more on this topic.)

2) A cooked mixture of dairy and meat.1

So pet food that does not contain both milk and meat is fine for year-round use.2 If, however, the product contains meat, then this product may only be used if it doesn't also contain milk (or a milk derivative, such as whey or casein).

I should point out, though, that the "meat" that we may not cook with milk, or may not benefit from if it was cooked with milk, is meat from a kosher animal.3 Therefore, if it can be determined that the meat in the pet food comes from a non-kosher animal (such as horse meat), then it is "kosher" for your pet.4

Rabbi Eliezer Danzinger for Chabad.org