The purpose of this study was to clarify the effect of reducing somatosensory feedback by foot cooling on the medial gastrocnemius muscle. Using a system identification technique, we estimated the natural frequencies of the muscle and the ankle joint. The natural frequencies are proportional to the square root of the muscle and joint stiffnesses and indicate the frequency characteristics of quiet standing. We measured the center of pressure (COP) of eight young volunteers aged 22-24 years before and after foot-cooling by immersing the feet in water with ice. Electrical stimulation was applied to the medial gastrocnemius muscle, and electrically induced COP fluctuation was extracted using a Kalman filter and synchronously averaged based on the stimulation. The synchronously averaged COP fluctuation was considered an impulse response, and the transfer function was identified using a singular value decomposition method. The natural frequencies were estimated from the poles of the transfer functions. The natural frequencies of the muscle before foot cooling ranged from 1.96 to 3.09 Hz, and those after foot cooling decreased to a range of 1.40 to 2.19 Hz. There was a significant difference (p < 0.01) between the natural frequencies before and after foot cooling. The natural frequencies of the ankle joint tended to decrease after foot cooling, although the difference was not significant. The natural frequency of the medial gastrocnemius muscle decreased significantly when foot cooling reduced somatosensory feedback in the feet.