I've practiced yoga for 15 years. It is a meditative exercise focused on stretching and the flow of movements with your breath. When I practice I pray to Heavenly Father, or to St. Mary, or to our Savior. One of my favorite meditative mantras is "Christ loves". I find saying the Hail Mary silently as I practice sun salutations to be extremely powerful.
Think of how so many of our prayers in the Church are meditative (I'm thinking particularly of the Rosary). Add to that defined movements and a quieting of the mind, and it is quite powerful. I always dedicate my practice to the Lord and I ask Him to guide my mind and body as I reach out in mental and physical prayer to Him.
Yoga, like many other things, is rooted in Hindu. yet I doubt you will find many accomplished yoga instructors who are practicing Hindi. There are many branches of yoga, and like all things, it is what you make it. Should we not do aerobics because it was popularized by Jane Fonda? Should we avoid Pilates because Joseph Pilates was an atheist? No. I think we can take a truly secular exercise and raise it up to the Lord as a higher practice.