No one particular degree is necessary.
Marketing is also good for the sales aspect, but even liberal arts is acceptable.
Volunteer for local sports events and organizations. Attend classes on PR and marketing, if only to network. Read trade magazines and job listings. Though I had worked in the publicity department of a major publishing house upon graduation from college with a degree in English literature, it was through an ad in The New York Times that I stumbled into the work of sports public relations and marketing. When I met with the president of this particular company, and admitted to him that I didn't know the difference between a helmet and a hat trick, I was hired on the spot for my strong media contacts, people skills, tenacity and enthusiasm.