If you're going it alone, congrats—no qualifications needed. Well, you need a finger to click the button. And it'd also help to have some contacts who might showcase your work. Otherwise, though, if you can prove you've got the photo-taking skills, that's all you need.
If you work for a studio, publication, or other company, they might want to you have a degree in photography or media arts. At the very least you'll need to have a professional portfolio put together. The shots you took in a photo booth at the San Diego Zoo, where you custom-angled the camera behind the curtain to create an obscured self-portrait, don't count.
No, not even if you were making a super funny face. The companies are going to want your best artistic and professional work. Zoo selfies don't fall into those categories.