There is nothing in Islam that says that one cannot take part in sports during Ramadan, given that such participation does not violate the fasting. Fasting in the month of Ramadan is one of the five pillars (arkan) of Islam. There are only a few valid reasons – such as illness for example – that excuse us from fasting in Ramadan. Even in such situations, the missed days must be made up as soon as possible following ‘Eid ul-Fitr. Unfortunately, playing sports is not one of those reasons.
As Muslims, Ramadan is a time for us to focus on self-reflection and a deeper level of our remembrance of Allah. However, this does not preclude us from continuing with our worldly affairs such as working, studying and the like. Many young Muslims, particularly in the West, participate in school sports during Ramadan. The famous Muslim basketball player Hakeem Olajuwan used to play professional basketball while keeping the fast of Ramadan. You can read about him on the Internet for more information. To sum up, there is nothing wrong with continuing to play sports in Ramadan, as long as one is confident that it will not affect his or her ability to maintain fasting.