For someone like Ramy Ashour, a top-ranked player on the professional squash circuit who travels two or three times every month of the year, the key to success on the courts is adaptability. “You have to get comfortable with being uncomfortable,” he says with a laugh.

He’s had plenty of practice. Mr. Ashour has been playing in international tournaments since he was 6. In 2010, he became one of the youngest players to reach a world No. 1 ranking and is currently ranked 5th after a big win at the men’s world squash championship in November. He was hoping to ride that success to a fourth win at the 2015 J.P. Morgan Tournament of Champions starting Jan. 16—the squash equivalent of Wimbledon—but a torn meniscus requiring immediate surgery will prevent him from competing. He plans to be courtside for the semifinals and finals at the specially constructed glass court in New York City’s Grand Central Terminal.

Mr. Ashour’s busy travel schedule was encouraged from an early age by his parents, longtime employees of EgyptAir (now retired), who wanted their sons to have the opportunity to see the world. His father thought squash could be their ticket. Mr. Ashour and his brother traveled from their home in Cairo to international tournaments accompanied by their mother. At age 16, Mr. Ashour was experienced enough to travel on his own.

He tends to travel light, in more ways than one. He’s known as one of the rare players at his level who travels without an entourage of coaches, physical therapists and masseurs. (A recent move to New York, where such experts are closer at hand than in Cairo, is designed to change that, especially in the aftermath of his upcoming surgery.)

Mr. Ashour considers mental focus crucial in squash, and a lot of his travel strategies involve maintaining it. He travels with a Quran, for example. “It makes me feel safe and secure. I’m not crazy religious, but it’s something that makes me feel better to have with me.” For many years he trained with music in the background, mostly Egyptian pop music. Now he just listens in his down time. “One day it just hit me that I want to listen to my voice, listen to my breath, listen to how I talk to myself when I play,” he says. “I’m trying to be more in the real world.”