Recently, a switch-based hybrid massive MIMO structure that aims to reduce the hardware complexity and power consumption has been proposed as a potential candidate for millimeter wave (mmWave) communications. In this paper, we investigate a matrix completion (MC)-based low-complexity channel estimator for such systems, which is compatible with the switch-based hybrid structure. We conduct a thorough comparison of the proposed scheme with state-of-the-art compressive sensing (CS)-based schemes. We show that our proposed scheme can achieve near-optimal spectral efficiency (SE) at significantly lower complexity. Furthermore, we demonstrate that the MC-based estimator, which does not need to assume a basis as required by CS estimators, is immune to array response mismatch which may arise from phase and amplitude errors.