We experimentally demonstrate the observation of a frequency-shift dynamics at a temporal boundary in the terahertz (THz) region relying on a scheme that controls the structural dispersion of a metalsemiconductor waveguide. Ultrafast structural-dispersion switching is achieved within a subpicosecond timescale by illuminating a waveguide surface with an optical pump pulse during the propagation of a THz pulse in the waveguide. Owing to the relatively high conversion efficiency, up to 23%, under the condition that the frequency shift is sufficiently larger than the bandwidth of the incident pulse, the rapid variation of the THz frequency around the temporal boundary is directly observed in the time domain.