This work uses surface acoustic waves (SAWs) that are generated by a piezoelectric substrate containing an interdigital transducer (IDT) to which a low voltage of 2 mV was applied at a frequency of 1 kHz to fabricate a polymer-stabilized blue phase liquid crystal (PS-BPLC) layer. The PS-BPLC layer has a more uniform optical microscope (OM) image at a voltage of 2 mV than at zero voltage, and its reflective spectrum exhibits a smaller full width at half maximum (FWHM) at the former than at the latter. The uniform OM image and small FWHM reveal that the lattices in the PS-BPLC layer have monodomain structure. The monodomain PS-BPLC layer is formed because the SAWs cause longitudinal and transverse vibrations of the PS-BPLC lattices in the vertical plane along their traveling direction. The proposed method for fabricating the monodomain PS-BPLC layer using the SAWs has potential for the development of reflective optical devices that consume low power during their fabrication.