Materials that exhibit colossal magnetoresistance (CMR) have attracted much attention due to their potential technological applications. One particularly interesting model for the magnetoresistance of low-carrier-density ferromagnets involves mediation by magnetic polarons (MP)-electrons localized in nanoscale ferromagnetic 'droplets' by their exchange interaction. However, MP have not previously been directly detected and their size has been difficult to determine from macroscopic measurements. In order to provide this crucial information, we have carried out muon spin rotation measurements on the magnetoresistive semiconductor Lu(2)V(2)O(7) in the temperature range from 2 to 300 K and in magnetic fields up to 7 T. Magnetic polarons with characteristic radius R ≈ 0.4 nm are detected below about 100 K, where Lu(2)V(2)O(7) exhibits CMR; at higher temperature, where the magnetoresistance vanishes, these MP also disappear. This observation confirms the MP-mediated model of CMR and reveals the microscopic size of the MP in magnetoresistive pyrochlores.