Basically no, and if you want to be a PT go for it. All kinds of people are PTs.
I'm Currently in PT school. A lot of people are athletically inclined, but it has more to do with the fact that everyone is fairly young and cares about their health. Some of my classmates that played sports in college have serious wear and tear (surgeries, osteoarthritis, flat feet, etc.). You probably would have trouble picking out who were the athletes and who weren't. People have all types of bodies; short, tall, chubby, skinny, muscular, and basically every variation. It's about knowing how to use your body. I've seen tiny skinny lady PTs move large patients through great technique and skill.
People also have all kinds of experiences that lead them to PT. It wasn't just through sports and many PTs work outside of sports type settings. Plenty of my classmates don't really care about sports. Your mind is just as important as your body.
You don't need to be some body builder or fitness freak. But you should probably have some kind of physical activity that keeps you health and is fun for you (you will need an outlet during PT school). One of my classmates is into salsa dancing and another is into outdoor activities like hiking.
