Millimeter wave (mmWave) massive multiple-input multiple-output (mMIMO) has been recognized as a promising candidate for 5G communications for its capability of supporting Gb/s transmission. However, it is a common exercise to deploy a limited number of radio-frequency (RF) chains at mmWave mMIMO transceivers due to hardware complexity and cost. As a result, the potential multiplexing gain (MG), which is restricted by the smaller number of RF chains at the transmitter and receiver, is markedly compromised. In order to boost the MG and spectral efficiency (SE), we innovatively develop a novel index modulation termed as the generalized beamspace modulation (GBM). The acquisition of (sub-)beamspace is owing to a natural exploitation of the unique features of mmWave mMIMO. Based on the (sub-)beamspace, a complete GBM transceiver is designed and optimized. Unlike existing alternatives that are largely digital based, our GBM is tailored for the hybrid structure of mmWave mMIMO and can, thereby, realize efficient spatial multiplexing despite the limited RF chains. Extensive analyses and simulations have demonstrated remarkable superiority of GBM over existing counterparts in terms of the error performance and SE.