Love for Nature
You must be someone who loves nature. That is a prerequisite as you will never be able to fully understand the whole process without some passion. You should be comfortable being outdoors and willing to live in tough and often not so conducive conditions.
Love for Adventure
You should be an adventurous person by nature and should be able to take photography in somewhat dangerous places as a challenge and an adventure. Unless you are ready for some crazy time, this may not be the job for you.
You must also possess some good photographic skills. Knowing how to handle the camera is not enough and you should also have a good sense when it comes to taking snaps. If you are able to capture the crux of the moment in a picture, you can very well be a successful wildlife photographer.
It is also not a bad idea to take some classes and do a course on wildlife photography. Like all fields within photography, wildlife has its own specific requirements and you should be at home with them. This will give you a very professional mindset from the start which can be very helpful in the long run.
Hands on Training
Once you have started it somewhat, it is not a bad idea to have some hands on training. Ideally join a well known wildlife photographer as an internee and go on some wildlife photography trips. This should give you a lot of exposure as to how the op guys do it and also will provide you with a chance to learn new aspects of the field. You should hone your skills with such an experience.