We numerically and experimentally demonstrate an ultrathin and compact Mach–Zehnder interferometer (MZI) for sensing and amplitude/phase modulations of spoof surface plasmon polariton (SSPP) waves. For a specific frequency, the magnitude and phase of the far-field transmission are modulated when a dielectric sample is loaded on one of the MZI arms. The phase difference between the SSPP waves propagating along the sensing and reference arms causes the outputs from both arms to interfere, allowing small perturbations in the sensing arm to be detected. Our study shows that the sensitivity of the proposed SSPP MZI is significantly higher than that of the single-armed SSPP waveguide, and also better than that of the conventional MZI formed with the traditional microstrip lines. The dependence of the sensitivity on the structural parameters such as geometrical parameters of the detected material and the arm length of MZI is discussed, revealing the possibility of realizing miniaturized MZI with high sensitivity.