Cadmium Telluride (CdTe), with its high photon absorption efficiency, has been regarded as a promising semiconductor material for the next generation X/γ-ray detectors. In order to apply this device to astrophysics, it is essential to investigate the radiation hardness and background properties induced by cosmic-ray protons in orbit. We irradiated Schottky CdTe diodes and a CdTe block with a beam of mono-energetic (150 MeV) protons. The induced activation in CdTe was measured externally with a germanium detector, and internally with the irradiated CdTe diode itself. We successfully identified most of radioactive isotopes induced mainly via (p, xn) reactions, and confirmed that the activation background level of CdTe diode is sufficiently low in orbit. We compared energy resolution and leakage current before and after the irradiation and also monitored the signals from a calibration source during the irradiation. There have been no significant degradation. CdTe diodes are tolerant enough to radioactivity in low earth orbit.