We obtained the first experimental evidence for the magnetohydrodynamic (MHD) nature of ionospheric medium-scale travelling wave packets (MSTWP). We used data on total electron content (TEC) measurements obtained at the dense Japanese network GPS/GEONET (1220 stations) in 2008-2009. We found that the diurnal, seasonal and spectral MSTWP characteristics are specified by the solar terminator (ST) dynamics. MSTWPs are the chains of narrow-band TEC oscillations with single packets duration of about 1-2 hours and oscillation periods of 10-20 minutes. Their total duration is about 4--6 hours. The MSTWP spatial structure is characterized by a high degree of anisotropy and coherence at the distance of more than 10 wavelengths. The MSTWP direction of travelling is characterized by a high directivity regardless of seasons. Occurrence rate of daytime MSTWPs is high in winter and during equinoxes. Occurrence rate of nighttime MSTIDs has its peak in summer. These features are consistent with previous MS travelling ionosphere disturbance (TID) statistics obtained from 630-nm airglow imaging observations in Japan. In winter, MSTWPs in the northern hemisphere are observed 3-4 hours after the morning ST passage. In summer, MSTWPs are detected 1.5-2 hours before the evening ST occurrence at the point of observations, at the moment of the evening ST passage in the magneto-conjugate point. Both the high Q-factor of oscillatory system and synchronization of MSTWP occurrence with the solar terminator passage at the point of observations and in the magneto-conjugate area testify the MHD nature of ST-excited MSTWP generation. The obtained results are the first experimental evidence for the hypothesis of the ST-generated ion sound waves.