Sheikh `Abd Allah b. Muhammad al-Tayyâr, professor at al-Qasîm University
It is permissible for a woman to engage in any such sporting activities with the permission of her guardian as long as those activities are of benefit to her and do not involve her in any of the following:
1. exposing her body to non-mahram men
2. near-nudity among other women
3. free mixing with men
4. physical harm to herself
If these conditions are met, then there is nothing wrong with her engaging in sporting activities similar to the practice related about the Prophet (peace be upon him) that he engaged in footraces with `A’ishah.
And Allah knows best.
Source: Islam Today