In short, yes. It is not the same disorder we as humans suffer from, as our brains are much more advanced and more of our brain is affected. Species of animals such as elephants and chimpanzees, found to have many social and neurobiological similarities with humans, have been found to suffer from this disorder.
PTSD describes anxiety based responses from witnessing life threatening responses. Animals are used quite often when it comes to studying the effects of certain events on a human's life, and many experiments have proved that they do, indeed, suffer from this disorder.
According to this, experiments have been undertaken to replicate torture, loss of a family member, and incarceration humans are exposed to during wartime.
Most elephants in these experiments have suffered from not just PTSD, but from many different stress disorders in captivity. They have been wrenched from their natural environment in which the communities that made up their lives previously are not there to comfort them.
It may be that wild animals can suffer from PTSD for a while, but most likely not for their full lives. Lone animals may suffer from this a little bit more than, say, an elephant in a herd will, so it is entirely possible that they can experience it.