From UX Matters:
A degree in user experience—or more likely, a degree in one of these specialties—provides you with an opportunity to learn this body of knowledge in a structured manner. Through course assignments and assessment of your work, you also have opportunities to put that knowledge into practice in a controlled and protected environment. A degree program also ensures that you don’t skip over parts, that you lay a solid foundation, and that you do, in fact, apply knowledge in practical ways.However, you’ll find that, if you ask most UX professionals with eight or more years of experience whether they have a directly relevant degree, they’ll answer no. They learned by doing; through trial and error; by reading, sharing, and putting what they learned into practice daily.