Mechanical tuning of defect modes in a polymer-based one-dimensional photonic crystal was demonstrated for the terahertz (THz) spectral range. A sharp defect mode in the photonic bandgap was achieved by symmetrically enclosing a defect layer with two identical pairs of alternating compact and low-density layers. By adjusting the thickness of the defect layer, the spectral position of the defect mode within the photonic bandgap was easily controlled. Normal incidence transmission spectroscopy in a spectral range from 82 to 125 GHz was used to determine the THz spectral response for different defect layer thicknesses. The transmission data were analyzed using stratified optical layer model calculations. Spectral shift of the center frequency of the narrow transmission peak within a distinct photonic bandgap was observed in the experimental transmission spectra. The shift was achieved by mechanical tuning of the defect layer thickness. A good agreement between the relevant model parameters and the corresponding design parameters was found.