We report measurements of low-temperature specific heat on the 4f^2-based heavy-fermion superconductor PrOs4Sb12. In magnetic fields above 4.5 T in the normal state, distinct anomalies are found which demonstrate the existence of a field-induced ordered phase (FIOP). The Pr nuclear specific heat indicates an enhancement of the 4f magnetic moment in the FIOP. Utilizing a Maxwell relation, we conclude that anomalous entropy, which is expected for a single-site quadrupole Kondo model, is not concealed below 0.16 K in zero field. We also discuss two possible interpretations of the Schottky-like anomaly at ~3 K, i.e., a crystalline-field excitation or a hybridization gap formation.